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: 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 rate of depreciation (in decimal), and $t$ is the time in years.

Step2: Convert the rate to decimal

The depreciation rate $r = 11.25\% = \frac{11.25}{100} = 0.1125$.

Step3: Substitute the values into the formula

We have $P = 19000$, $r = 0.1125$, and $t = 14$. So, $V = 19000(1 - 0.1125)^{14}$.

Step4: Calculate $(1 - 0.1125)$

$1 - 0.1125 = 0.8875$.

Step5: Calculate $0.8875^{14}$

Using a calculator, $0.8875^{14} \approx 0.1946$.

Step6: Calculate the final value

$V = 19000 \times 0.1946 \approx 3697.40$.

Answer:

The value of the car after 14 years will be approximately $\$3697.40$.