Sam purchases a new car for $21,000 and it depreciates in value each year. The function y=21,000(1−0.15)^x

Question

represents the depreciation. To the nearest dollar, what will be the value of the car after 5 years?(1 point)
Responses

$21,000
$21,000

$15,000
$15,000

$10,000
$10,000

$9,318

Answer 1

To find the value of the car after 5 years using the function \( y = 21,000(1 - 0.15)^x \), we will substitute \( x \) with 5:

\[ y = 21,000(1 - 0.15)^5 \]

First, calculate \( 1 - 0.15 \):

\[ 1 - 0.15 = 0.85 \]

Now, raise this value to the power of 5:

\[ 0.85^5 \approx 0.4437 \]

Next, multiply this result by 21,000:

\[ y \approx 21,000 \times 0.4437 \approx 9,316.77 \]

Rounding to the nearest dollar:

\[ y \approx 9,317 \]

Therefore, the value of the car after 5 years is approximately $9,318.

So the correct response is:

$9,318.