Question

a new car is purchased for 17300 dollars. the value of the car depreciates at 9.25% per year. what will the value of the car be, to the nearest cent, after 15 years?

Explanation:

Step1: Recall the exponential decay formula

The formula for exponential decay is $V(t) = V_0(1 - r)^t$, where $V_0$ is the initial value, $r$ is the rate of decay (as a decimal), and $t$ is the time in years.
Here, $V_0 = 17300$, $r = 0.0925$ (since 9.25% = 0.0925), and $t = 15$.

Step2: Substitute the values into the formula

Substitute the given values into the formula: $V(15) = 17300(1 - 0.0925)^{15}$.
First, calculate $1 - 0.0925 = 0.9075$.
Then, calculate $0.9075^{15}$. Using a calculator, $0.9075^{15} \approx 0.2342$.
Then, multiply by 17300: $17300 \times 0.2342 \approx 4051.66$.

Answer:

The value of the car after 15 years will be approximately $\$4051.66$.