SOLUTION: write an exponential function that includes (2,20)(0,5)

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Question 406573: write an exponential function that includes (2,20)(0,5)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose our exponential function is in the form

f%28x%29+=+ab%5Ex, where a and b are nonzero constants. Since f(0) = 5, then

5+=+ab%5E0 --> a = 5.

Also, since f(2) = 20, we can substitute and get 20+=+5%2A%28b%5E2%29 --> b = 2 (the solution b = -2 is somewhat extraneous because it's not easily defined on real numbers, and not exponential). Therefore we can write f%28x%29+=+5%2A2%5Ex.