SOLUTION: Find the exponential function f(x)= Ca ^x which contains the points (2,45) and (5,1215) please show work i would like to learn this process thanks

Algebra ->  Functions -> SOLUTION: Find the exponential function f(x)= Ca ^x which contains the points (2,45) and (5,1215) please show work i would like to learn this process thanks      Log On


   

Question 213273: Find the exponential function f(x)= Ca ^x which contains the points (2,45) and (5,1215)
please show work i would like to learn this process thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
f%28x%29+=+Ca%5Ex
(2,45)
(5,1215)
I'll make 2 equations by substituting these values
(1) 45+=+Ca%5E2
(2) 1215+=+Ca%5E5
Multiply both sides of (1) by a%5E3
(1) 45a%5E3+=+Ca%5E5
And substituting again,
(2) 1215+=+45a%5E3
a%5E3+=+1215%2F45
a%5E3+=+27
a+=+3
(1) 45+=+Ca%5E2
45+=+C%2A9
C+=+5
The equation is
f%28x%29+=+5%2A3%5Ex answer
check:
1215+=+5%2A3%5E5
1215+=+5%2A243
1215+=+1215
OK
45+=+5%2A3%5E2
45+=+5%2A9
45+=+45
OK