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
$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.