Answer :
To determine the growth factor of the function \( f(x) = \frac{1}{3} (6)^x \), we need to identify the base of the exponential term.
Here’s a step-by-step breakdown:
1. Consider the function \( f(x) = \frac{1}{3} (6)^x \).
2. In any exponential function of the form \( a \cdot b^x \):
- \( a \) is a constant coefficient.
- \( b \) is the base of the exponential term, known as the growth factor.
3. In the given function \( f(x) \), the coefficient \( a \) is \(\frac{1}{3}\), and the base \( b \) (which is the growth factor) is \( 6 \).
Therefore, the growth factor of the function [tex]\( f(x) = \frac{1}{3} (6)^x \)[/tex] is [tex]\( 6 \)[/tex].
Here’s a step-by-step breakdown:
1. Consider the function \( f(x) = \frac{1}{3} (6)^x \).
2. In any exponential function of the form \( a \cdot b^x \):
- \( a \) is a constant coefficient.
- \( b \) is the base of the exponential term, known as the growth factor.
3. In the given function \( f(x) \), the coefficient \( a \) is \(\frac{1}{3}\), and the base \( b \) (which is the growth factor) is \( 6 \).
Therefore, the growth factor of the function [tex]\( f(x) = \frac{1}{3} (6)^x \)[/tex] is [tex]\( 6 \)[/tex].
