The function [tex]$f(x)=2 \cdot 5^x[tex]$[/tex] can be used to represent the curve through the points [tex]$[/tex](1,10)[tex]$[/tex], [tex]$[/tex](2,50)[tex]$[/tex], and [tex]$[/tex](3,250)$[/tex].

What is the multiplicative rate of change of the function?

A. 2
B. 5
C. 10
D. 32



Answer :

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].