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Consider the function [tex]f(x) = \frac{1}{3}(6)^x[/tex]. What is the value of the growth factor of the function?

Sagot :

GinnyAnswer
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].
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