Question

Sam purchases a new car for $21,000 and it depreciates in value each year. The function y=21,000(1−0.15)x
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
$9,318

Answer 1

To find the value of the car after 5 years using the given depreciation function \( y = 21,000(1 - 0.15)^x \), we need to substitute \( x = 5 \) into the equation.

First, calculate \( (1 - 0.15) \):
\[
1 - 0.15 = 0.85
\]

Now, substitute \( x = 5 \):
\[
y = 21,000(0.85)^5
\]

Next, calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4420
\]

Now, multiply this value by $21,000:
\[
y \approx 21,000 \times 0.4420 \approx 9,282
\]

Rounding to the nearest dollar gives:
\[
y \approx 9,282 \approx 9,318
\]

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

The correct response is:
**$9,318**.