SOLUTION: Find the exponential function of the given form that contains the given points. Form: f(x)= c*(a^x) Points: (0,4) and (4, 324) I know the answer is f(x)=4*3^x, Please explain,

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the exponential function of the given form that contains the given points. Form: f(x)= c*(a^x) Points: (0,4) and (4, 324) I know the answer is f(x)=4*3^x, Please explain,       Log On


   

Question 1000525: Find the exponential function of the given form that contains the given points.
Form: f(x)= c*(a^x)
Points: (0,4) and (4, 324)
I know the answer is f(x)=4*3^x,
Please explain, thanks!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If (0,4) is a point on the graph of then or . Since any number to the zero power is 1, we know that .

If (4,324) is a point on the graph of , then or . But we know that , so , which is to say .

All you need now is to find the value of which is the 4th root of 81.

John

My calculator said it, I believe it, that settles it