Question

question
a new car is purchased for 20700 dollars. the value of the car depreciates at 11% 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: Define depreciation formula

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

Step2: Identify given values

$P = 20700$, $r = 0.11$, $t = 11$

Step3: Substitute values into formula

$V = 20700(1 - 0.11)^{11}$

Step4: Calculate the decay factor

First compute $1 - 0.11 = 0.89$, then $0.89^{11} \approx 0.2774$

Step5: Compute final value

$V \approx 20700 \times 0.2774$
$V \approx 5742.18$

Answer:

$\$5742.18$