Question

a new car is purchased for 19000 dollars. the value of the car depreciates at 11.25% 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 $P$ is initial value, $r$ is annual depreciation rate, $t$ is time in years.

Step2: Identify given values

$P = 19000$, $r = 0.1125$, $t = 14$

Step3: Substitute values into formula

$A = 19000(1 - 0.1125)^{14}$

Step4: Calculate the decay factor

$1 - 0.1125 = 0.8875$

Step5: Compute the power term

$0.8875^{14} \approx 0.1874$

Step6: Calculate final value

$A = 19000 \times 0.1874 \approx 3560.60$

Answer:

3560.60 dollars