# Given the exponential function A(x) = P(1 + r)^x, what value for r will make the function a decay...

## Question:

Given the exponential function A{eq}(x) = P(1 + r)^x {/eq}, what value for r will make the function a decay function?

## Exponential Function:

An exponential function is of the form: {eq}A(x) = P(1 + r)^x {/eq}. Here, {eq}P {/eq} is the initial value and {eq}r {/eq} is the rate of growth or the rate of decay.

• This represents a growth function if {eq}r>0 {/eq}.
• This represents a decay function if {eq}-1<r<0 {/eq}.

Become a Study.com member to unlock this answer!

The given exponential function is:

$$A(x) = P(1+r)^x$$

For this to be a decay function:

0<1+r<1\\ \text{Subtracting 1 from all the...