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
Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. $$\displaystyle{f{{\left({t}\right)}}}={80}{\left(\frac{{3}}{{5}}\right)}^{{t}}$$

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: $$r=0.4$$