Question

Filipe bought a classic car, originally valued at $70,000, in 2006. He believes that the value of the car depreciates exponentially at a rate of 4% each year. Round the expected value of Filipe's car in 2018 to the nearest dollar. Enter your answer in the box. $

Answer 1

so, from 2006 to 2018 is 12 years then,

$\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &70000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=\textit{elapsed time}\dotfill &12\\ \end{cases} \\\\\\ A=70000(1-0.04)^{12}\implies A=70000(0.96)^{12} \\\\\\ A\approx 42889.68\implies A=\stackrel{rounded~up}{42890}$