Question

Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. f(t)=80(3/5)^t

Exponential growth and decay
ANSWERED
asked 2021-07-04
Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change.
\(\displaystyle{f{{\left({t}\right)}}}={80}{\left(\frac{{3}}{{5}}\right)}^{{t}}\)

Answers (1)

2021-07-05

We are given the function: \(\displaystyle{y}={80}{\left(\frac{{3}}{{5}}\right)}^{{t}}\)
The function is in the form: \(\displaystyle{y}={a}{\left({1}-{r}\right)}^{{t}}\), where \(1-r<1\)
Thus the function represents exponential decay.
Using the decay factor 1-r, we find the rate of decay r: \(\displaystyle{1}-{r}=\frac{{3}}{{5}}={0.6}\)
\(r=1-0.6\)
\(r=0.4=40\%\)

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