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.
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.
The value of a car as a function of time after it was purchased is best modeled with an exponential function.
This is because the depreciation of a car's value over time typically follows an exponential decay pattern. When a car is new, it experiences the most significant drop in value, referred to as "instant depreciation." As time goes on, the rate of depreciation slows down.
Using a linear function to model the value of a car would imply a constant rate of depreciation, which is not the case in reality. Similarly, a quadratic function would suggest that the rate of depreciation increases with time, which is also inaccurate.
An exponential function, on the other hand, captures the gradual decline in value experienced by a car over time. It is the most realistic and accurate representation of the relationship between a car's value and the elapsed time since its purchase.