To find the growth factor of the exponential function [tex]\( f(x) = \frac{1}{5} \left( 15^x \right) \)[/tex], let’s break down the function into its components.
The general form of an exponential function is [tex]\( f(x) = a \cdot b^x \)[/tex], where:
- [tex]\( a \)[/tex] is a constant coefficient.
- [tex]\( b \)[/tex] is the base of the exponential term [tex]\( b^x \)[/tex], which determines the growth factor.
- [tex]\( x \)[/tex] is the variable exponent.
In the given function [tex]\( f(x) = \frac{1}{5} \left( 15^x \right) \)[/tex]:
- The coefficient [tex]\( a \)[/tex] is [tex]\(\frac{1}{5}\)[/tex].
- The exponential term has a base [tex]\( b \)[/tex] of [tex]\( 15 \)[/tex].
The growth factor of an exponential function is given by the base [tex]\( b \)[/tex] of the exponential expression [tex]\( b^x \)[/tex].
Therefore, for the function [tex]\( f(x) = \frac{1}{5} \left( 15^x \right) \)[/tex], the growth factor is [tex]\( 15 \)[/tex].
Thus, the value of the growth factor is:
[tex]\[ 15 \][/tex]
