Question: : Last week we worked on a regression problem (the pizza problem). This week let’s focus on exponential models. Cars depreciate in value as soon as you take them out of the showroom. A certain car originally cost $25,000. After one year, the car’s value is $21,500. Assume that the value of the car is decreasing exponentially; that is, assume that the ratio of the car’s value in one year to the car’s value for the previous year is constant.

(a) Find the ratio: worth after one year/ original worth

(b) What is the car’s value after two years? After ten years?

(c) Approximately when is the car’s value half of its original value?

(d) Approximately when is the car’s value one-quarter of its original value?

(e) If you continue these assumptions, will the car ever be worth $0? Explain.