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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. $

Respuesta :

so, from 2006 to 2018 is 12 years then,


[tex]\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}[/tex]

The expected value of Filipe's car in 2018 to the nearest dollar is  $42,890.

What is the expected value of Filipe's car in 2018?

Depreciation occurs when the price of an item declines with the passage of time.

The formula for calculating future value when there is a depreciation is:

FV = P (1 - r)^n

  • FV = Future value
  • P = Present value
  • R = rate of depreciation
  • N = number of years

$70,000 x ( 1 - 0.04)^12 = $42,890

To learn more about future value, please check: https://brainly.com/question/18760477

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