Question

# Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. f(t)=1/3(1.26)^t

Exponential growth and decay
Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change.
$$\displaystyle{f{{\left({t}\right)}}}=\frac{{1}}{{3}}{\left({1.26}\right)}^{{t}}$$

2021-05-31
We are given the function: $$\displaystyle{f{{\left({t}\right)}}}=\frac{{1}}{{3}}{\left({1.26}\right)}^{{t}}$$
The function represents exponential growth because 1.26>1.
We rewrite the function in the form $$\displaystyle{y}={a}{\left({1}+{t}\right)}^{{t}}$$: $$\displaystyle{y}=\frac{{1}}{{3}}{\left({1}+{0.26}\right)}^{{t}}$$
We determine the rate of change: r=0.26