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 :

Answer:

6,400

Step-by-step explanation:

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

450 times 8=3600

10,000-3600=6400

[tex]\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 \frac{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[/tex]