SOLUTION: Suppose g is an exponential function and g(2)=10 and g(3)=19. Write a function formula for g.

Algebra ->  Finance -> SOLUTION: Suppose g is an exponential function and g(2)=10 and g(3)=19. Write a function formula for g.       Log On


   

Question 1153796: Suppose g is an exponential function and g(2)=10 and g(3)=19. Write a function formula for g.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


g%28x%29+=+a%2Ab%5Ex%29

g(2) = 10 --> ab%5E2+=+10 [1]
g(3) = 19 --> ab%5E3+=+19 [2]

Divide [2] by [1]: b+=+19%2F10+=+1.9

We could plug that value of b in [1] to find the value of a:

a%2819%2F10%29%5E2+=+10
a+=+10%2F%28361%2F100%29+=+1000%2F361

The function is then

g%28x%29+=+%281000%2F361%29%2819%2F10%29%5Ex

It is probably "nicer" if we use x=2 for the "reference point"; that will give us the equivalent function

g%28x%29+=+10%2A%2819%2F10%29%5E%28x-2%29
or
g%28x%29+=+10%2A1.9%5E%28x-2%29