Fit exponential with constant I have data whic would fit to an exponential function with a constant. 

$$y=a\cdot\exp(b\cdot t) + c.$$

Now I can solve an exponential without a constant using least square by taking log of y and making the whole equation linear. Is it possible to use least square to solve it with a constant too ( i can't seem to convert the above to linear form, maybe i am missing something here) or do I have to use a non linear fitting function like nlm in R ?
A direct method of fitting (no guessed initial values required, no iterative process) is shown below.
For the theory, see the paper (pp.16-17) : https://fr.scribd.com/doc/14674814/Regressions-et-equations-integrales
I tried to deduce the formula for 'b' in case of equdistant ti-s, but I have got a different one. There is a reciprocal under the logarithm in my result. (Please check it. Maybe I am not right.)

Sorry. I see ... The t3-t1 minus sign makes the log content right.