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.
$$\displaystyle{f{{\left({t}\right)}}}={80}{\left(\frac{{3}}{{5}}\right)}^{{t}}$$

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: $$\displaystyle{1}-{r}=\frac{{3}}{{5}}={0.6}$$
$$r=1-0.6$$
$$r=0.4=40\%$$