9 Multiple Choice 10 points The price of a car that was bought for \( \$ 20,000 \) has depreciated \( 8 \% \) yearly. Write a model to describe the value of the car. \[ \begin{aligned} f(t) & =20,000(0.08)^{t} \\ f(t) & =20,000(1.08)^{t} \\ f(t) & =20,000(0.92)^{t} \\ f(t) & =20,000(1.92)^{t}\end{aligned} \]

To model the value of the car over time, you need to account for the depreciation, which means that the value decreases each year. Since the car loses 8% of its value annually, you retain 92% of its value each year. Thus, the correct model is: \[ f(t) = 20,000(0.92)^{t} \] This means that for every year \( t \), the value of the car is the original price, \( \$20,000 \), multiplied by \( 0.92 \) raised to the power of \( t \). Now, imagine buying a new car. Over time, as you drive it, its value drops faster than you can say "depreciation!" Embracing this concept is essential when considering resale value. When selling, remember to check reliable sources or calculators that can help estimate your car's current worth based on its age and condition—those resources can be your best friends!