Question

An intitial population of 745 quail increases at an annual rate of 16%. Write an exponential function to model the quail population. What will the approximate population be after 4 years?

Answer 1

$\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &745\\ r=rate\to 16\%\to \frac{16}{100}\to &0.16\\ t=\textit{elapsed time}\to &t\\ \end{cases} \\\\\\ A=745(1+0.16)^t$

and after 4 years?  well, t = 4, so    $\bf A=745(1+0.16)^4$