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 2021-05-31
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)

2021-06-01

We are given the function: \(\displaystyle{f{{\left({t}\right)}}}={80}{\left(\frac{{3}}{{5}}\right)}^{{t}}\)
The function represents exponential decay because \(\displaystyle{\left(\frac{{3}}{{5}}\right)}{<}{1}\). We rewrite the function in the form \(\displaystyle{y}={a}{\left({1}-{t}\right)}^{{t}}\)
\(\displaystyle{y}={80}{\left({1}-{\left(\frac{{2}}{{5}}\right)}\right)}^{{t}}={80}{\left({1}-{0.4}\right)}^{{t}}\)
We determine the rate of change: \(r=0.4\)

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