Question

11.

A new car bought for $18,000 depreciates at the rate of 14.3% per year,
a. Write a function that models the value of the car.
b. Find the value of the car after three 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 &18000\\ r=rate\to 14.3\%\to (14.3)/(100)\dotfill &0.143\\ t=years \end{cases} \\\\\\ A=18000(1 - 0.143)^(t)\implies A=18000(0.857)^t \\\\\\ \textit{3 years later, t = 3}\qquad A=18000(0.857)^3\implies A\approx 11329.61`