Question

consider the exponential function $f(x) = \frac{1}{5}(15^x)$. what is the value of the growth factor of the function?

$\circ \\ \frac{1}{5}$

$\circ \\ \frac{1}{3}$

$\circ \\ 5$

$\circ \\ 15$

Explanation:

Step1: Recall the form of exponential function

The general form of an exponential function is \( f(x) = a(b^x) \), where \( a \) is the initial value and \( b \) (with \( b>0, b
eq1 \)) is the growth or decay factor. If \( b > 1 \), it is a growth factor; if \( 0 < b < 1 \), it is a decay factor.

Step2: Identify the components of the given function

The given function is \( f(x)=\frac{1}{5}(15^x) \). Comparing this with the general form \( f(x) = a(b^x) \), we can see that \( a=\frac{1}{5} \) and \( b = 15 \).

Answer:

D. 15