Question

Alex purchased a new car for $28000. The cars value depreciates 7.25% each year. What will be the value of the car 5 years after it is purchased? Round your answer to the nearest dollar

Answer 1

`\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &28000\\ r=rate\to 7.25\%\to (7.25)/(100)\to &0.0725\\ t=\textit{elapsed time}\to &5\\ \end{cases} \\\\\\ A=28000(1-0.0725)^5\implies A=28000(0.9275)^5 \\\\\\ A\approx 19218.859982795703125`