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
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
Answers
GPT-4o mini
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**.
\[
y = 21,000(1 - 0.15)^5
\]
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**.