Hello Cem,
As has been mentioned you can use the curve fitting toolbox for this job, but if you don't have it you can try a simple linear fit. If
y = b*e^(ax), then log(y) = log(b) + ax
and the linear fit is of log(y) vs. x. Here is a quick example. Too be somewhat realistic, to the exponential y = e^(ax) is added a nonzero baseline (which is pretty common), a function that is proportonal to 20x near the origin, and some noise. The curve fitting toolbox will do better, but this fit is better than I thought it would be.
Whether the fit is great or not, I think a linear fit to log(y) is always worth doing, just to see if the idea of fitting an exponential to the given data is in the ballpark in the first place.
y = b/3 + 20*x./(1+x) + b*exp(a*x) + b*r;
is an exponential function, thus it does not exhibit a logarithmic trend.
