Question

consider the function $f(x) = \frac{1}{3}(6)^x$. what is the value of the growth factor of the function? 18, 2, 6, $\frac{1}{3}$

Explanation:

Step1: Recall exponential function form

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

Step2: Identify components of given function

For the function \( f(x)=\frac{1}{3}(6)^x \), compare it to \( f(x) = a(b)^x \). Here, \( a=\frac{1}{3} \) and \( b = 6 \). The growth factor is \( b \), so we identify \( b \) from the function.

Answer:

6 (corresponding to the option with value 6)