SOLUTION: Find formula fo f(x), an exponential function such that f(2)= 1/27 and f(-1)=27

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Question 1164989: Find formula fo f(x), an exponential function such that f(2)= 1/27 and f(-1)=27
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




John

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

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The general exponential function is

f%28x%29+=+ab%5Ex

Make two equations in a and b using the two data points.

1%2F27+=+ab%5E2
27+=+ab%5E%28-1%29

In both equations, the coefficient is a, so dividing one equation by the other will give you an equation in b only. (That's a standard procedure for finding an exponential function given two data points.)

%281%2F27%29%2F27=+b%5E3
1%2F729+=+b%5E3
b+=+1%2F9

Use that value with either data point to determine the coefficient a.

1%2F27+=+a%28%281%2F9%29%5E2%29
1%2F27+=+a%2F81
a+=+3

ANSWER: f%28x%29+=+ab%5Ex+=+3%28%281%2F9%29%5Ex%29