Question

mathematics i a-g cr sem a aguirre
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 general form of an exponential function is \( f(x) = a(b^x) \), where \( b \) is the growth (or decay) factor, and \( a \) is the vertical stretch/shrink factor.

Step2: Identify Components in Given Function

For the function \( f(x) = \frac{1}{5}(15^x) \), compare it to \( f(x) = a(b^x) \). Here, \( a = \frac{1}{5} \) (vertical stretch/shrink) and \( b = 15 \) (growth factor).

Answer:

15