A new car is purchased for 17000 dollars. The value of the car depreciates at \( 13.5 \% \) per year. What will the value of the car be, to the nearest cent, after 12 years?

To calculate the value of the car after 12 years of depreciation, we can use the formula for exponential decay: \[ V = P(1 - r)^t \] where: - \( V \) is the future value of the car, - \( P \) is the initial value of the car ($17,000), - \( r \) is the depreciation rate (0.135), and - \( t \) is the time in years (12). Plugging in the values: \[ V = 17000(1 - 0.135)^{12} = 17000(0.865)^{12} \] Calculating \( 0.865^{12} \): \[ 0.865^{12} \approx 0.277 \] Now, calculating the future value: \[ V \approx 17000 \times 0.277 \approx 4719.00 \] Therefore, the value of the car after 12 years will be approximately **$4,719.00**.