Respuesta :
Answer:
The multiplicative rate of change for the exponential function is 0.4.
Step-by-step explanation:
Given : Exponential function [tex]f(x) = 2(\frac{5}{2})^{-x}[/tex]
To find : The multiplicative rate of change for the exponential function.
Solution :
The general form of exponential function is
[tex]f(x)=ab^x[/tex]
where b is the rate of change of the function.
First we write the given function in proper form :
[tex]f(x) = 2(\frac{5}{2})^{-x}[/tex]
[tex]f(x) = 2(\frac{2}{5})^{x}[/tex]
The rate of change is [tex]\frac{2}{5}=0.4[/tex]
Therefore, The multiplicative rate of change for the exponential function is 0.4.
Answer:
0.4
Step-by-step explanation:
We have been given an exponential function [tex]f(x)=2(\frac{5}{2})^{-x}[/tex]. We are asked to find the multiplicative rate of change.
We will use exponent properties to solve our given problem.
Using property [tex](\frac{a}{b})^{-1}=(\frac{b}{a})^x[/tex], we can rewrite our given function as:
[tex]f(x)=2(\frac{2}{5})^{x}[/tex]
[tex]f(x)=2(0.4)^{x}[/tex]
We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,
a = Initial value,
b = Multiplicative rate of change.
Upon looking at our given function, we can see that the value of b is 0.4, therefore, the multiplicative rate of change for the given exponential function is 0.4.
