Answer:
The multiplicative rate of change is [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Here, the given function,
[tex]f(x)=2(\frac{5}{2})^{-x}[/tex]
[tex]=2(\frac{5^{-x}}{2^{-x}}[/tex]
[tex]=2(\frac{2^x}{5^x}[/tex]
[tex]\implies f(x)=2(\frac{2}{5})^x[/tex]
Which is an exponential function,
Since, in an exponential function [tex]f(x)=ab^x[/tex]
b is called growth factor or multiplicative rate of change,
By comparing,
b = 2/5,
Hence, The multiplicative rate of change of the given function is [tex]\frac{2}{5}[/tex]
