It seems to me you have an array of data points (xi, yi) from an experiment, and you want to fit the data to your model equation, thus obtaining a, b, and c for the best fit.
Have a look at the "Nonlinear Levenberg-Marquardt fit".
The embedded "factory default function" is:
y= a0*exp(a1*x)+a2;
You should be able to use it after some small modifications.