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.
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