Used cars are often sold wholesale at auctions, and from these sales, retail sales prices are recommended. The following table gives the recommended prices in 2009 for a four-door manual transmission Toyota Corolla based on the age of the car.
Age (in years), x Suggested retail price, y
1……………………………$14,680
2…………………………… 12,150
3…………………………… 11,215
4…………………………… 10,180
5…………………………… 9,230
6…………………………… 8,455
7…………………………… 7,730
8…………………………… 6,825
9…………………………… 6,135
10………………………….. 5,620
(a) Fit these data with a model of the form y = aebx. Graph the (xi, yi)’s and superimpose the least squares exponential curve.
(b) What would you predict the retail price of an eleven year- old Toyota Corolla to be?
(c) The price of a new Corolla in 2009 was $16,200. Is that figure consistent with the widely held belief that a new car depreciates substantially the moment it is purchased? Explain.