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):
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
.