Question

A tree frog population doubles every 5 weeks. Suppose that currently, there are 21 tree frogs in your backyard. How many tree frogs will there be in 15 weeks?

Answer 1

since we know the population is doubling, that means the rate of growth is 100%, whatever it was before, 100% more, every 5 weeks, so

`\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{(t)/(c)}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &21\\ r=rate\to 100\%\to (100)/(100)\dotfill &1.00\\ t=weeks\dotfill &15\\ c=period\to &5 \end{cases} \\\\\\ A=21(1 + 1.00)^{(15)/(5)}\implies A=21(2)^3\implies A=168`