To determine the multiplicative rate of change of the exponential function \( f(x) = 2 \cdot 5^x \), we need to identify the base of the exponent.
1. The given function is \( f(x) = 2 \cdot 5^x \).
2. In an exponential function of the form \( f(x) = a \cdot b^x \):
- \( a \) is the initial value or coefficient.
- \( b \) is the base of the exponential, which represents the multiplicative rate of change.
3. In our function, \( f(x) = 2 \cdot 5^x \):
- The coefficient \( a \) is 2.
- The base \( b \) is 5.
4. The base \( b \), which is 5, is the multiplicative rate of change of the function. This means that for each unit increase in \( x \), the value of the function \( f(x) \) is multiplied by 5.
Therefore, the multiplicative rate of change of the function [tex]\( f(x) = 2 \cdot 5^x \)[/tex] is [tex]\(\boxed{5}\)[/tex].
