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 initial principal (purchase price), $r$ is the annual depreciation rate (in decimal), and $t$ is the time in years.
Here, $P = 19000$, $r = 11.25\% = 0.1125$, and $t = 14$.

Step2: Substitute the values into the formula

Substitute the given values into the formula: $V = 19000(1 - 0.1125)^{14}$.
First, calculate $(1 - 0.1125) = 0.8875$.
Then, calculate $0.8875^{14}$. Using a calculator, $0.8875^{14} \approx 0.1946$.
Now, multiply by the initial price: $V = 19000 \times 0.1946 \approx 3697.4$.

Answer:

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