Question

Write an equation for an exponential growth function where the initial population is 74 and the population quadruples during each time period.

Answer 1

If the population quadruples every period say hour, that means the "rate of growth" is 300%, so whatever the current amount, increased by 3 times as much is 4 times the current amount, or a quadrupled amount.

$\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &74\\ r=rate\to 300\%\to \frac{300}{100}\to &3.00\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=74(1+3)^t\implies A=74(4)^t$