To determine the growth factor of the exponential function [tex]\( f(x) = \frac{1}{5} \left(15^x\right) \)[/tex], we need to focus on the base of the exponent [tex]\( x \)[/tex].
An exponential function is generally of the form [tex]\( f(x) = A \cdot B^x \)[/tex], where:
- [tex]\( A \)[/tex] is a constant coefficient,
- [tex]\( B \)[/tex] is the base of the exponent and represents the growth factor.
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 base [tex]\( B \)[/tex] is 15.
The growth factor is identified by the base of the exponent term, which is 15 in this function.
Thus, the value of the growth factor is [tex]\( \boxed{15} \)[/tex].
