On Mon, Nov 22, 2010 at 11:37 AM, Martin Maxino
<address@hidden> wrote:
or is f_0 a parameter too? oh no. im confused. lol
so f_0 and a are the parameters right?
but i already have data, and at t=0, f(t) = f_0 = something. Am i still
supposed to treat f_0 as an unknown parameter?
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Usually you do, because you assume that your measurements are noisy, otherwise you could simply take two points and solve a system of equations to find the parameters. So, if you have f(t) = f_0.*exp(-a*t), then you can do the first approach I mentioned, take the natural log of your measurements, so your model then looks like:
log(f(t)) = log(f_0) - a*t
then do a linear regression (polyfit of order 1) on this transformed measurement, so you'd get
log(f(t)) = m*x + b
(I used m this time to not get confused with your "a" variable).
then to calculate a and f_0:
a = -m
f_0 = exp(b)