Is the value of a car as a function of time after it was purchased best modeled with a linear function, a quadratic function, or an exponential function? Explain.

Answer 1

The value of a car as a function of time after it was purchased is best modeled with an exponential function. This is because a car's value generally depreciates at a faster rate in the early years and then slows down over time. As time goes on, the value of the car becomes a smaller and smaller fraction of its original value. Therefore, an exponential decay model is more appropriate to capture the depreciation of the car's value over time. Linear and quadratic functions assume a constant rate of change in the value of the car over time, which is not accurate.