Answer:
The multiplicative rate of change is [tex]\dfrac{2}{5}.[/tex]
Step-by-step explanation:
You are given the function
[tex]f(x)=2\cdot \left(\dfrac{5}{2}\right)^{-x}[/tex]
First, use the following property of exponents
[tex]\left(\dfrac{a}{b}\right)^{-x}=\left(\dfrac{b}{a}\right)^{x}[/tex]
So, your function is
[tex]f(x)=2\cdot \left(\dfrac{2}{5}\right)^{x}[/tex]
If the exponential function is written in the form
[tex]f(x)=a\cdot b^x,[/tex]
then b is the multiplicative rate of change for this exponential function.
In your case, the multiplicative rate of change is [tex]\dfrac{2}{5}.[/tex]
