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?

Explanation:

Step1: Define depreciation formula

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

Step2: Plug in given values

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

Step3: Calculate the decay factor

First compute $1 - 0.1175 = 0.8825$
Expression: $0.8825^{11} \approx 0.2704$

Step4: Compute final value

Multiply initial value by the decay factor
Expression: $V = 17600 \times 0.2704$

Answer:

$4759.04$ dollars