You certainly could try using FindFit[], but I think I should also mention Forman Acton's words on the matter:
One of the perennial problems that plagues, among others, the analyzers of isotope decay is the fitting of data by a series of exponential functions. How much of
$A$ and how much of
$B$, decaying at known rates
$a$ and
$b$, are in the sample whose activity was sampled at several times in the historic past? This question is quite tractable. Computationally we are being asked to fit only the parameters
$A$ and
$B$ in the equation $$y = Ae^{-at} + Be^{-bt}$$ when we have observed a sample at several times to produce a set of
$\{t_i, Y_i\}$ pairs. It is a simple least-squares fit that generally requires only a desk calculator.
Unfortunately there is a companion problem that looks only slightly more complicated—until you try it! We again have
$\{t_i, Y_i\}$ readings from a radioactive sample, but the decaying materials are not known, hence the decay rates
$a$ and
$b$ must also be fitted. The answer to this problem lies in the chemical rather than the computer laboratory, and the sooner the hopeful innocent can be sent there and away from the computer room, the better off everyone will be. For it is well known that an exponential equation of this type in which all four parameters are to be fitted is extremely ill conditioned. That is, there are many combinations of
$(a, b, A, B)$ that will fit most exact data quite well indeed (will you believe four significant figures?) and when experimental noise is thrown into the pot, the entire operation becomes hopeless. But those with Faith in Science do not always read the Book—and must be spanked or counselled. At the very least, keep them from obstructing Progress and the computer!
