How to estimate data plots as an exponential with a horizontal Asymptote? y=Ax^B+C where B<1

I am trying to find what my data will equal as x tends towards infinity, This should be possible by estimating the plots as y=Ax^B+C where B<1. I have 4 data sets which should all theoretically have the same value for C but diferent A and B values.

Below are my code and the errors;

Code:

syms A B C; % equation coefficient symbols to be solved

x=[0.5 1 2 3];

y=[292.4 264.8 324 305; 182.2 175.6 202.4 199.6; 108.8 112.6 113.2 124.3; 79.8 82.7 94.2 97.6];

for i=1:4

[solA, solB, solC] = solve(A*x(1)^B + C == y(1,i), A*x(2)^B + C == y(2,i), A*x(3)^B + C == y(3,i), A*x(4)^B + C == y(4,i));

% convert the symbolic answers into numerical form

A_vals(i) = double(solA);

B_vals(i) = double(solB);

C_vals(i) = double(solC);

end

Errors

Unable to perform assignment because the left and right sides have a

different number of elements.

Error in Project (line 8)

A_vals(i) = double(solA);

Thank You

Answer 1

[Sam Chak]

Hi @Dominic Bruce

Are you looking for something like this?

x  = [0.5 1 2 3];
y  = [292.4 264.8 324 305; 182.2 175.6 202.4 199.6; 108.8 112.6 113.2 124.3; 79.8 82.7 94.2 97.6];

fo = fitoptions('Method','NonlinearLeastSquares',...
               'Lower',[300, 0, 50],...
               'Upper',[500, Inf, 100],...
               'StartPoint',[400 1 75]);
ft = fittype('a*exp(-x/b) + c', 'options', fo);

for j = 1:4
    [curve, gof] = fit(x', y(:,j), ft);
    A(j) = curve.a;
    B(j) = curve.b;
    C(j) = curve.c;
    plot(x, y(:,j), 'o'), hold on
end
a = mean(A);
b = mean(B);
c = mean(C)     % horizontal asymptote

c = 82.8209

x = linspace(0.5, 3, 2501);
y = a*exp(-x/b) + c;
plot(x, y, '--', 'linewidth', 1.5, 'Color', '#528AF9'), hold off, grid on
xlabel('x'), ylabel('y')