Question

question
a new car is purchased for 17600 dollars. the value of the car depreciates at 11.75% per year. what will the value of the car be, to the nearest cent, after 11 years?
answer attempt 1 out of 2

Explanation:

Step1: Identify depreciation formula

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

Step2: Plug in values

$P = 17600$, $r = 0.1175$, $t = 11$. So $V = 17600(1 - 0.1175)^{11}$.

Step3: Calculate remaining value factor

$1 - 0.1175 = 0.8825$. Compute $0.8825^{11} \approx 0.2609045$.

Step4: Find final value

$17600 \times 0.2609045 \approx 4591.92$.

Answer:

4591.92