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Algebra II - Growth and Decay Factor











































For an annual rate of change of -31%, find the corresponding growth or decay factor

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Apr 05, 2011
Algebra II - Growth and Decay Factor
by: Staff


The question:

For an annual rate of change of -31%, find the corresponding growth or decay factor


The answer:

The annual rate of change for your problem is a constant: -31% per year.

The function which describes a constant % rate of change is called an exponential function.

It has the form:

f(t) = (initial value)*(1 + rate of change)^t


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Definitions:

t = time in years

(1 + rate of change) is called the “growth factor” if its value is greater than 1.

(1 + rate of change) is called the “decay factor” if its value is less than 1, but greater than 0.


(1 + rate of change)^t = (1 + rate of change) raised to the “t” power

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For your problem

f(t) = (initial value)*(1 + rate of change)^t

f(t) = (initial value)*(1 – 31%)^t

f(t) = (initial value)*(1 – .31)^t

f(t) = (initial value)*(0.69)^t

(1 + rate of change) = 0.69 < 1 = decay factor

The decay factor is: 0.69


The final answer: The decay factor is: 0.69




Thanks for writing.


Staff
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