Textbook Problem

Automobile CostsThe data in the table show the variable costs of operating an automobile in the United States for 2000 through 2010, where t is the year, with t = 0 corresponding to 2000. The functions y₁, y₂ and y₃ represent the costs in cents per mile for gas, maintenance, and tires, respectively. (Source: Bureau of Transportation Statistics)

t	y1	>2	y3
0	6.9	3.6	1.7
1	7.9	3.9	1.8

2	5.9	4.1	1.8
3	7.2	4.1	1.8
4	6.5	5.4	0.7
5	9.5	4.9	0.7
6	8.9	4.9	0.7
7	11.7	4.6	0.7
8	10.1	4.6	0.8
9	11.4	4.5	0.8
10	12.3	4.4	1.0

(a) Use the regression capabilities of a graphing utility to find cubic models for y₁ and y₃, and a quadratic model for y₂.

(b) Use a graphing utility to graph y₁, y₂, y₃, and y₁ + y₂+ y₃ in the same viewing window. Use the model to estimate the total variable cost per mile in 2014.