Question

What is the multiplicative rate of change for the exponential function f(x) = 2(5/2)-x

Answer 1

0.4

Explanation:

We have been given an exponential function
`f(x)=2((5)/(2))^(-x)`. We are asked to find the multiplicative rate of change.

We will use exponent properties to solve our given problem.

Using property
`((a)/(b))^(-1)=((b)/(a))^x`, we can rewrite our given function as:

`f(x)=2((2)/(5))^(x)`

`f(x)=2(0.4)^(x)`

We know that an exponential function is in form
`y=a\cdot b^x`, 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.

Answer 2

The multiplicative rate of change for the exponential function is 0.4.

Explanation:

Given : Exponential function
`f(x) = 2((5)/(2))^(-x)`

To find : The multiplicative rate of change for the exponential function.

Solution :

The general form of exponential function is

`f(x)=ab^x`

where b is the rate of change of the function.

First we write the given function in proper form :

`f(x) = 2((5)/(2))^(-x)`

`f(x) = 2((2)/(5))^(x)`

The rate of change is
`(2)/(5)=0.4`

Therefore, The multiplicative rate of change for the exponential function is 0.4.