Question

Determine if the function f(x) =3^2x-3is exponential. If it is exponential, determine the base, b, when the function is written in the form f(x) = ab^x

Answer 1

Given the exponential function:

$f(x)=3^{2x-3}$

notice that we can write it in the ab^x form in the following way:

$f(x)=3^{2x-3}=3^{-3}\cdot3^{2x}=3^{-3}\cdot(3^2)^x=3^{-3}(9)^x^{}$

therefore, b = 9