Fitting different gradients of an exponential curve

I want to fit a varying array of exponential curves between two set points on a graph but im not sure how to do this.

Currently the closest i have is shown in the image, which is done through just generating an exponential equation between differnt end points and then adding the end value to the end of all vectors so that they are the same length.. but this makes the graphs have big kinks in them. is there a better way to do this?

Thanks.

Example code:

 V0 = 300;
 Z_end = 100;
 Z = (1:1:Z_end);

 V_exp_100 = V0+ ((Vmax - V0)/log(Z_end))*log(Z); 
 plot(V_exp_100,-Z)