@pagan : If that's the case, then I think there is no finite optimal solution. If we take c fixed for the moment, we can get optimal values for a and b by running
Statistics:-ExponentialFit(ln~([3.05, 3.1, 3.75] -~ c), [.74e-4, .1806e-3, .584e-4]);
(at least, optimal in a slightly perturbed metric). We can find the minimal sum of squared residuals for a given value of c as follows:
minsumsq := c -> Statistics:-ExponentialFit(ln~([3.05, 3.1, 3.75] -~ c),
[.74e-4, .1806e-3, .584e-4]);
It now appears that minsumsq keeps decreasing as c goes to minus infinity (and the corresponding a and b go to plus infinity and minus infinity, respectively). Thus, there's no optimal solution.
Hope this helps,