Solve for coefficients of $y = A(1 - e^{-x/B})$ given two points

Question

I have the equation $y = A(1 - e^{-x/B})$, and two $(x,y)$ pairs. How can I solve for $A$ and $B$? This should be simple, but I've been banging my head against the algebra for a while to no avail.

I should probably mention that this is not homework.

Answer 1

If you have two particular points, $(x_1, y_1)$, and $(x_2, y_2)$, then you have two equations and two unknowns: $$A=\frac{y_1}{1-e^{-x_1/B}}$$ $$B=-x_2\left(\ln\left(\frac{y_2-A}{-A}\right)\right)^{-1}$$ Since $x_1$, $y_1$, $x_2$, and $y_2$ are constants, this is like solving an a regular two equation to unknown algebra problem, albeit a nasty one.