Question

The sales at a particular bookstore grew from $2090 million in 2000 to $3849 million in 2005. Find an exponential function to model the sales as a function of years since 2000. Give your answer using the form B=Boat

Answer 1

`\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &2090\\ I=\textit{initial amount}\\ r=rate\to r\%\to (r)/(100)\\ t=\textit{elapsed time}\to &0\\ \end{cases} \\\\\\ 2090=I(1+r)^0\implies 2090=I\\\\ -------------------------------\\\\`


`\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &3849\\ I=\textit{initial amount}\to &2090\\ r=rate\to r\%\to (r)/(100)\\ t=\textit{elapsed time}\to &\stackrel{2000-2005}{5}\\ \end{cases}`


`\bf 3849=2090(1+r)^5\implies \cfrac{3849}{2090}=(1+r)^5\implies \sqrt[5]{\cfrac{3849}{2090}}=1+r \\\\\\ \sqrt[5]{\cfrac{3849}{2090}}-1=r\implies 0.129900823\approx r\implies 0.13\approx r\\\\ -------------------------------\\\\ A=2090(1+0.13)^t\implies \boxed{A=2090(1.13)^t}`