The value of a car purchased new for \( \$ 36,000 \) decreases by \( 3.25 \% \) each year. a) Write the exponential function. b) What will be the approximate value of the car in 8 years? Round your answer to the nearest dollar.

a) The value of the car can be modeled by the exponential function \( V(t) = 36000 \times (1 - 0.0325)^t \), where \( V(t) \) is the value of the car at time \( t \) in years. b) To find the car's value in 8 years, plug in \( t = 8 \): \( V(8) = 36000 \times (1 - 0.0325)^8 \approx 36000 \times 0.7491 \approx 26963 \). Thus, the approximate value of the car in 8 years is \( \$ 26,963 \). Ever wonder how car depreciation can impact your finances? Like a sneaky ninja, it creeps in stealthily! Cars typically lose value quickly in the first few years—often up to 20% of their purchase price! Knowing how these percentages play out can be key during your next car purchase, so keep this in mind for budgeting. If you’re contemplating buying a new car, you might want to consider leasing as an alternative. Unlike purchasing, leasing can often yield a newer vehicle every few years without the concerns of long-term depreciation. This means you get to enjoy that "new car smell" and the latest tech without the hefty price tag!