Question

vertical stretches and shrinks of exponential functions
consider the exponential function ( f(x) = \frac{1}{5}(15^x) ). what is the value of the growth factor of the function?
options: ( \frac{1}{5} ), ( 5 ), ( \frac{1}{3} ), ( 15 )

Explanation:

Step1: Recall exponential function form

The standard form of an exponential growth function is $f(x) = a(b^x)$, where $a$ is the initial value/vertical scale factor, and $b$ (where $b>1$) is the growth factor.

Step2: Match given function to form

The given function is $f(x) = \frac{1}{5}(15^x)$. Comparing to $f(x)=a(b^x)$, we identify $b=15$. The vertical scale factor $\frac{1}{5}$ does not affect the growth factor.

Answer:

15