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.
Since we have tow points
We know for our problem that
Now, we just need to find
Dividing equation (2) by equation (1):
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
