Initial values of a exponential decay

Question

How can I estimate the initials values ($A$, $B$, $C$) of a exponential decay? I got the function and a set of experimental points.

$p(t) = Ae^{-1.5t} + Be^{-0.3t} + Ce^{0.05t}$

$p(0.5)=6,\ p(1)=4.4,\ p(2)=3.2,\ p(3)=2.7,\ p(4)=2,\ p(5)=1.9,\ p(6)=1.7,\ p(7)=1.4,\ p(9)=1.1$

Thanks

Answer 1

If the function is indeed the sum of three exponentials of known time constants, this is a simple case of linear fitting which can be solved by least squares.

Answer 2

See the computation sheet below (linear regression) :

Answer 3

If the problem is just to identify $A,B,C$ to get the best fit of $$p = Ae^{-1.5t} + Be^{-0.3t} + Ce^{0.05t}$$ on the basis of $n$ data points $(t_i,p_i)$, there is no need of initial estimates. Define intermediate variables $$u_i=e^{-1.5t_i}\quad , \quad v_i=e^{-0.3t_i}\quad , \quad w_i=e^{0.05t_i}$$ which make the model to be $$p=A u+B v+C w$$ which corresponds to a multilinear regression with no intercept.