Question

Maggie bought a new car for $14,000. It has depreciated in value at an annual rate of 12%. What is the value of the car after 5 years? Write your answer to the nearest cent.

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 &14000\\ r=rate\to 12\%\to (12)/(100)\dotfill &0.12\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 14000(1 - 0.12)^(5) \implies A = 14000( 0.88 )^(5)\implies A \approx 7388.25`