Question

Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. f(x) = 2060 ⋅ 0.9906x

Exponential growth function; 0.0094%

Exponential decay function; -0.94%

Exponential decay function; 0.0094%

Exponential growth function; -0.94%

Answer 1

Exponential decay function; -0.94%

Explanation:

we have

`f(x)=2,060(0,9906)^x`

This is a exponential function of the form

`y=a(b)^x`

where

a is the initial value or the y-intercept

b is the base of the exponential function

If b > 1 we have a exponential growth function

If b < 1 we have a exponential decay function

r is the percentage rate of change

b=(1+r)

In this problem we have

`a=2,060`

`b=0,9906` ----> is a exponential decay function

`r=b-1=0.9906-1=-0.0094`

Convert to percentage

`-0.0094*100=-0.94\%`

therefore

Exponential decay function; -0.94%