SOLUTION: Express the function in the form f(x) = 5(1/3)^2x-1 in the form f(x) = a•d^-x

Question 1180949: Express the function in the form f(x) = 5(1/3)^2x-1 in the form f(x) = a•d^-x

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The function you show is not an exponential function:

f(x) = 5(1/3)^2x-1 is

It's astonishing to me how few students who post questions about this level of math seem to realize that the proper use of parentheses is important...!

Nevertheless, there is some good algebra to be learned here; so I will go ahead and work with the function you INTENDED to show.

f(x) = 5(1/3)^(2x-1) =

We are to write this as an equivalent function in the form

To do that, we need to get rid of the "2" and the "-1" in the exponent.

To get rid of the "-1" in the exponent, multiply AND divide the expression by (1/3):

The expression is now

To make the exponent x instead of 2x, use the power-to-a-power rule:

ANSWER:

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