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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}.

Answer and Explanation: 1

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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...

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Exponential Growth vs. Decay

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Chapter 10 / Lesson 2
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What is an exponential growth function? Learn the exponential growth and exponential decay formulas and find out what growth and decay graphs look like.


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