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: Identify the formula for depreciation

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

Step2: Convert the percentage to a decimal

The depreciation rate $r = 12.25\% = 0.1225$.

Step3: Substitute the values into the formula

We have $P = 17000$, $r = 0.1225$, and $t = 14$. So, $V = 17000(1 - 0.1225)^{14}$.

Step4: Calculate $(1 - 0.1225)$

$1 - 0.1225 = 0.8775$.

Step5: Calculate $0.8775^{14}$

Using a calculator, $0.8775^{14} \approx 0.1749$.

Step6: Calculate the final value

$V = 17000 \times 0.1749 \approx 2973.30$.

Answer:

The value of the car after 14 years will be approximately $\$2973.30$.