Question

When the town of Samuel Village first started its voluntary recycling program, 1200 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 35% each year. Which explicit rule can be used to determine the number of people participating in the program in the fifth year?

Answer 1

$\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &1200\\ r=rate\to 35\%\to \frac{35}{100}\to &0.35\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=1200(1+0.35)^t\implies A=1200(1.35)^t\implies \stackrel{\textit{fifth year}}{A=1200(1.035)^5}$