Question

The population of a town is increasing at a rate of 3.5% per year. In 2010, the town had a population of 24,500. Find the population of the town in 2021. (if you can please give a short explanation)

Answer 1

well, from 2010 to 2021  is 11 years later, so

$\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &24500\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &11\\ \end{cases} \\\\\\ A=24500(1 + 0.035)^{11}\implies A=24500(1.035)^{11}\implies A\approx 35769$