Question

the value of a car is $15,000 and depreciates at a rate of 8% per year. what is the exponential equation that models this situation? y = 15,000(1.08)^x y = 15,000(0.08)^x y = 8(15,000)^x y = 15,000(0.92)^x

Explanation:

Step1: Recall depreciation formula

The general exponential depreciation formula is $y = P(1 - r)^x$, where $P$ is initial value, $r$ is depreciation rate, $x$ is time in years.

Step2: Identify given values

$P = 15000$, $r = 0.08$

Step3: Calculate remaining value factor

$1 - r = 1 - 0.08 = 0.92$

Step4: Substitute into formula

$y = 15000(0.92)^x$

Answer:

D. $y = 15,000(0.92)^x$