Question

a new car is purchased for 17000 dollars. the value of the car depreciates at 12.25% per year. what will the value of the car be, to the nearest cent, after 14 years?

Explanation:

Step1: Define depreciation formula

The formula for exponential depreciation is $A = P(1 - r)^t$, where:

• $P = 17000$ (initial value),
• $r = 0.1225$ (annual depreciation rate),
• $t = 14$ (time in years).

Step2: Substitute values into formula

$A = 17000(1 - 0.1225)^{14}$

Step3: Calculate the decay factor

First compute $1 - 0.1225 = 0.8775$, then $0.8775^{14} \approx 0.1501$

Step4: Compute final value

$A = 17000 \times 0.1501 \approx 2551.70$

Answer:

$\$2551.70$