We are going to use the basic form of an exponential function:

to solve this problem.
Since we have tow points

and

, we are going to have a system of equations:

equation (1)

equation (2)
We know for our problem that

,

,

, and

, so lets replace those values in our equations:

equation (1)

equation (2)
Now, we just need to find

and

:
Dividing equation (2) by equation (1):


![b= \sqrt[3]{64}](https://tex.z-dn.net/?f=b%3D%20%5Csqrt%5B3%5D%7B64%7D%20)

equation (3)
Replacing equation (3) in equation (1):




Finally, we can put our function together:


We can conclude that the exponential function whose graph passes through the points (2,8) and (5,512) is

.