Question

a new car is purchased for 16200 dollars. the value of the car depreciates at 14.25% per year. what will the value of the car be, to the nearest cent, after 6 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

$P = 16200$, $r = 0.1425$, $t = 6$

Step3: Substitute values into formula

$A = 16200(1 - 0.1425)^6$

Step4: Calculate the decay factor

$1 - 0.1425 = 0.8575$

Step5: Compute the power term

$0.8575^6 \approx 0.400447$

Step6: Find final value

$A = 16200 \times 0.400447 \approx 6487.24$

Answer:

6487.24 dollars