Question

a new car is purchased for 20300 dollars. the value of the car depreciates at 9.5% 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 exponential depreciation is $A = P(1 - r)^t$, where $P$ is initial value, $r$ is annual depreciation rate, $t$ is time in years, and $A$ is final value.

Step2: Identify given values

$P = 20300$, $r = 0.095$, $t = 11$

Step3: Calculate remaining value factor

$1 - r = 1 - 0.095 = 0.905$

Step4: Compute $(0.905)^{11}$

$(0.905)^{11} \approx 0.35207$

Step5: Find final car value

$A = 20300 \times 0.35207$
$A \approx 7147.02$

Answer:

7147.02 dollars