{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60808,"title":"Estimating Battery Lifetime Based on Load Profile and Depth of Discharge (DoD)","description":"In a Battery Management System (BMS), the lifetime of a battery depends on various factors, including the Depth of Discharge (DoD), load profile, and the battery's cycle life. The cycle life of a battery is the number of complete charge-discharge cycles the battery can undergo before its capacity falls below a certain percentage of its original capacity (e.g., 80%).\r\nThe lifetime of the battery can be estimated using the following formula:\r\n\r\nWhere:\r\n​ is the battery lifetime in years (assuming one full charge-discharge cycle per day)\r\n is the number of charge-discharge cycles the battery can undergo before its capacity drops below 80%\r\nDoD is the Depth of Discharge (in percentage, e.g., 80%)\r\nIn this problem, you are given: \r\nThe cycle life of the battery\r\nThe DoD     for the battery (how much percentage of the battery’s total capacity is being used)\r\nThe load profile (which indicates how often the battery is being charged and discharged during a day)\r\nYou are asked to compute the battery lifetime using the given data and assumptions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 538.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 269.312px; transform-origin: 407px 269.312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBattery Management System (BMS)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the lifetime of a battery depends on various factors, including the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDepth of Discharge (DoD)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, load profile, and the battery's \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecycle life\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecycle life\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a battery is the number of complete charge-discharge cycles the battery can undergo before its capacity falls below a certain percentage of its original capacity (e.g., 80%).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe lifetime of the battery can be estimated using the following formula:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 71.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 35.9px; text-align: left; transform-origin: 384px 35.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"155\" height=\"66\" style=\"vertical-align: baseline;width: 155px;height: 66px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 26.0375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 13.0125px; transform-origin: 391px 13.0188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 13.0125px; text-align: left; transform-origin: 363px 13.0188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cimg class=\"imageNode\" width=\"54\" height=\"20\" style=\"vertical-align: baseline;width: 54px;height: 20px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e​ is the battery lifetime in years (assuming one full charge-discharge cycle per day)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 24.0375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 12.0125px; transform-origin: 391px 12.0188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 12.0125px; text-align: left; transform-origin: 363px 12.0188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cimg class=\"imageNode\" width=\"67\" height=\"18\" style=\"vertical-align: baseline;width: 67px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the number of charge-discharge cycles the battery can undergo before its capacity drops below 80%\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDoD is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDepth of Discharge\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (in percentage, e.g., 80%)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, you are given:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecycle life\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the battery\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDoD\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     for the battery (how much percentage of the battery’s total capacity is being used)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eload profile\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (which indicates how often the battery is being charged and discharged during a day)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are asked to compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ebattery lifetime\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e using the given data and assumptions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T_lifetime = estimateBatteryLifetime(cycleLife, DoD, dailyCycles)\r\n    % Calculate the battery lifetime based on the given parameters\r\n    T_lifetime = (cycleLife / (1 + (DoD / 100))) / dailyCycles;\r\nend\r\n","test_suite":"%% Test 1: Lower DoD (gentler discharge)\r\n% For cycle life = 1500, DoD = 50%, daily cycles = 1\r\n% Expected result: 1500 / (1 + 0.50) = 1000 cycles; lifetime = 1000 / 1 = 1000 years\r\nassert(abs(estimateBatteryLifetime(1500, 50, 1) - 1000) \u003c 0.01)\r\n\r\n%% Test 2: Higher DoD (faster discharge)\r\n% For cycle life = 800, DoD = 90%, daily cycles = 1\r\n% Expected result: 800 / (1 + 0.90) = 421.05 cycles; lifetime = 421.05 / 1 = 421.05 years\r\nassert(abs(estimateBatteryLifetime(800, 90, 1) - 421.05) \u003c 0.01)\r\n\r\n%% Test 3: Considering multiple daily cycles (e.g., high-use scenario)\r\n% For cycle life = 1000, DoD = 70%, daily cycles = 2\r\n% Expected result: 1000 / (1 + 0.70) = 588.24 cycles; lifetime = 588.24 / 2 = 294.12 years\r\nassert(abs(estimateBatteryLifetime(1000, 70, 2) - 294.12) \u003c 0.01)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":383919,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":273,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-02-14T17:01:53.000Z","updated_at":"2026-04-01T20:07:47.000Z","published_at":"2025-02-14T17:01:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBattery Management System (BMS)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lifetime of a battery depends on various factors, including the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDepth of Discharge (DoD)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, load profile, and the battery's \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecycle life\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecycle life\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of a battery is the number of complete charge-discharge cycles the battery can undergo before its capacity falls below a certain percentage of its original capacity (e.g., 80%).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe lifetime of the battery can be estimated using the following formula:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"66\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"155\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"20\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"54\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e​ is the battery lifetime in years (assuming one full charge-discharge cycle per day)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"67\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis the number of charge-discharge cycles the battery can undergo before its capacity drops below 80%\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDoD is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDepth of Discharge\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (in percentage, e.g., 80%)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are given:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecycle life\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the battery\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDoD\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e     for the battery (how much percentage of the battery’s total capacity is being used)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eload profile\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (which indicates how often the battery is being charged and discharged during a day)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are asked to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebattery lifetime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e using the given data and assumptions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image2.png\",\"relationshipId\":\"rId2\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image3.png\",\"relationshipId\":\"rId3\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAAXCAMAAACieZgxAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjpmOjqQOmaQOma2OpC2OpDbZgAAZgBmZjoAZmZmZmaQZpC2ZpDbZrbbZrb/kDoAkDpmkGY6kGaQkNv/tmYAtmY6tmZmtpA6ttvbttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2/9vb//+2///bS8zfHgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABrUlEQVRIS+1UbVPCMAxupu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Battery Lifetime Based on Load Profile and Depth of Discharge (DoD)","description":"In a Battery Management System (BMS), the lifetime of a battery depends on various factors, including the Depth of Discharge (DoD), load profile, and the battery's cycle life. The cycle life of a battery is the number of complete charge-discharge cycles the battery can undergo before its capacity falls below a certain percentage of its original capacity (e.g., 80%).\r\nThe lifetime of the battery can be estimated using the following formula:\r\n\r\nWhere:\r\n​ is the battery lifetime in years (assuming one full charge-discharge cycle per day)\r\n is the number of charge-discharge cycles the battery can undergo before its capacity drops below 80%\r\nDoD is the Depth of Discharge (in percentage, e.g., 80%)\r\nIn this problem, you are given: \r\nThe cycle life of the battery\r\nThe DoD     for the battery (how much percentage of the battery’s total capacity is being used)\r\nThe load profile (which indicates how often the battery is being charged and discharged during a day)\r\nYou are asked to compute the battery lifetime using the given data and assumptions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 538.625px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 269.312px; transform-origin: 407px 269.312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBattery Management System (BMS)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the lifetime of a battery depends on various factors, including the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDepth of Discharge (DoD)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, load profile, and the battery's \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecycle life\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecycle life\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of a battery is the number of complete charge-discharge cycles the battery can undergo before its capacity falls below a certain percentage of its original capacity (e.g., 80%).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe lifetime of the battery can be estimated using the following formula:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 71.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 35.9px; text-align: left; transform-origin: 384px 35.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"155\" height=\"66\" style=\"vertical-align: baseline;width: 155px;height: 66px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 26.0375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 13.0125px; transform-origin: 391px 13.0188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 13.0125px; text-align: left; transform-origin: 363px 13.0188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cimg class=\"imageNode\" width=\"54\" height=\"20\" style=\"vertical-align: baseline;width: 54px;height: 20px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e​ is the battery lifetime in years (assuming one full charge-discharge cycle per day)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 24.0375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 12.0125px; transform-origin: 391px 12.0188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 12.0125px; text-align: left; transform-origin: 363px 12.0188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cimg class=\"imageNode\" width=\"67\" height=\"18\" style=\"vertical-align: baseline;width: 67px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the number of charge-discharge cycles the battery can undergo before its capacity drops below 80%\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDoD is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDepth of Discharge\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (in percentage, e.g., 80%)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, you are given:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ecycle life\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the battery\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDoD\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     for the battery (how much percentage of the battery’s total capacity is being used)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eload profile\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (which indicates how often the battery is being charged and discharged during a day)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are asked to compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ebattery lifetime\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e using the given data and assumptions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T_lifetime = estimateBatteryLifetime(cycleLife, DoD, dailyCycles)\r\n    % Calculate the battery lifetime based on the given parameters\r\n    T_lifetime = (cycleLife / (1 + (DoD / 100))) / dailyCycles;\r\nend\r\n","test_suite":"%% Test 1: Lower DoD (gentler discharge)\r\n% For cycle life = 1500, DoD = 50%, daily cycles = 1\r\n% Expected result: 1500 / (1 + 0.50) = 1000 cycles; lifetime = 1000 / 1 = 1000 years\r\nassert(abs(estimateBatteryLifetime(1500, 50, 1) - 1000) \u003c 0.01)\r\n\r\n%% Test 2: Higher DoD (faster discharge)\r\n% For cycle life = 800, DoD = 90%, daily cycles = 1\r\n% Expected result: 800 / (1 + 0.90) = 421.05 cycles; lifetime = 421.05 / 1 = 421.05 years\r\nassert(abs(estimateBatteryLifetime(800, 90, 1) - 421.05) \u003c 0.01)\r\n\r\n%% Test 3: Considering multiple daily cycles (e.g., high-use scenario)\r\n% For cycle life = 1000, DoD = 70%, daily cycles = 2\r\n% Expected result: 1000 / (1 + 0.70) = 588.24 cycles; lifetime = 588.24 / 2 = 294.12 years\r\nassert(abs(estimateBatteryLifetime(1000, 70, 2) - 294.12) \u003c 0.01)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":383919,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":273,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-02-14T17:01:53.000Z","updated_at":"2026-04-01T20:07:47.000Z","published_at":"2025-02-14T17:01:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBattery Management System (BMS)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lifetime of a battery depends on various factors, including the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDepth of Discharge (DoD)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, load profile, and the battery's \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecycle life\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecycle life\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of a battery is the number of complete charge-discharge cycles the battery can undergo before its capacity falls below a certain percentage of its original capacity (e.g., 80%).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe lifetime of the battery can be estimated using the following formula:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"66\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"155\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"20\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"54\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e​ is the battery lifetime in years (assuming one full charge-discharge cycle per day)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"67\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis the number of charge-discharge cycles the battery can undergo before its capacity drops below 80%\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDoD is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDepth of Discharge\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (in percentage, e.g., 80%)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, you are given:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecycle life\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the battery\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDoD\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e     for the battery (how much percentage of the battery’s total capacity is being used)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eload profile\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (which indicates how often the battery is being charged and discharged during a day)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are asked to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebattery lifetime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e using the given data and 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