Question

16 friz purchased a car for $21,000. the value of the car depreciates at a rate of 14% per year. which equation below represents the value of the car, v, after 3 years? a ( v = 21,000(1.14)^3 ) b ( v = 21,000(0.14)^3 ) c ( v = 3(0.86)^{21,000} ) d ( v = 21,000(0.86)^3 )

Explanation:

Step1: Identify depreciation formula

The formula for exponential depreciation is $v = P(1 - r)^t$, where $P$ is initial value, $r$ is depreciation rate, $t$ is time in years.

Step2: Plug in given values

$P = 21000$, $r = 0.14$, so $1 - r = 0.86$, $t = 3$. Substitute into formula:
$v = 21000(0.86)^3$

Answer:

D. $v = 21,000(0.86)^3$