There are a few inefficiencies that I see. Firstly, you shouldn't pick an arbitrary StartPoint like [0.8,0.8]. The problem can be log-transformed into a linear equation and solved algebraically for a much more informed initial guess,
xdata=tr;
ydata=1-is_t1(:,i);
z=[x(:), ones(size(xdata(:)))]\log(ydata);
a0=-z(1)*var_c;
b0=exp(z(2));
In fact, depending on your needs and the noisiness of your data, the above analytical solution might be accurate enough already. Maybe you don't need to use an iterative routine like fit() after all.
But if the data noise is significant and you wish to further refine a0 and b0 with iterative nonlinear fitting, I would recommend fminspleas
which will let you iterate over a only,
modelfun=@(a) exp((-a/var_c)*x);
[a,b] = fminspleas({modelfun}, a0, xdata,ydata);
Notice also that we've optimized the implementation of your modelfun() a bit. Here, it only executes 2 vectorized operations whereas your original implementation had 5.
