Question

8. The population of a town is 10,000 and is decreasing at a rate of 4.5% per year.

Find the population of the town after 8 years.

Answer 1

`\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &10000\\ r=rate\to 4.5\%\to (4.5)/(100)\dotfill &0.045\\ t=\textit{elapsed time}\dotfill &8\\ \end{cases} \\\\\\ A=10000(1-0.045)^8\implies A=10000(0.955)^8\implies A\approx 6918`

Answer 2

6,400

Explanation:

10,000 times 0.045=450 (4.5% of 10,000=450)

450 times 8=3600

10,000-3600=6400