Exponential equation for three known points This answer (https://math.stackexchange.com/a/680695/438808) was helpful to me in finding the quadratic equation for three known points. 

Is there a similar solution for finding the exponential equation (y = ab^x + c) for three known points?

Thanks in advance!
For certain x-values of points that you're given, you may not be able to solve for the value of $b$ because when you set up a system, a polynomial will be formed with $b$ and polynomials with large degrees aren't necessarily solvable. However, here is a formula for an exponential function passing through any two points $(m,n)$ and $(p,q)$ no matter what the value of $b$ is:

$y=\frac{q-n}{b^p-b^m}(b^x-b^m)+n$

If you can get this through two of your points then you may be able to approximate a value for b.
You can find the base, $b$ by dividing equally separated differences.
if $q - p = n - m$ then
$b^{p-m} = (f(q) - f(p)) / ((f(n)-f(m))$

once you have the base, $b$, you can find the added constant.

$c = (b^{m-n}f(n) - f(m)) / (b^{m-n} -1)$