Problem

Interpret the percent decay in exponential model \(A(t)=800(0.9)^t\).

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What this problem is really about

For decay, the base represents the fraction retained each interval, while the loss is its complement to one. We’ll classify the base between zero and one, convert the retained fraction to a percent, subtract it from the whole, and state the resulting decrease per interval.

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The model shows a 10% decrease per interval because 0.9 means 90% of the amount remains each time, so 10% is lost.

The model shows a 90% decrease per interval because the factor 0.9 tells you the amount goes down by 90% each time.

The model shows a 9% decrease per interval because the decimal 0.9 means the decay rate is 9 out of 100 each time.

The model shows a 10% increase per interval because the 0.1 found from 1-0.9 gives the rate, and rates are written as growth.

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Interpret the percent decay in exponential model \(A(t)=800(0.9)^t\).

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