select the best model.
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1. The following gives the price in dollars of a round trip ticket from Phoenix to Portland, and the corresponding profit, in millions of dollars, for each price. For the data below, select the best model.
Price (dollars) 200 250 300 350 400 450
3.09 3.51 3.75 3.81 3.71 3.36
a. y= -3.721 x2 + 0.025 x -0.494
b. y = 0.0011x + 3.165
c. y = -2.148 x 10-8 x3 -1.627 x 10-5 x2 + 0.019x + 0.155
d. y = -3.721 x 10-5 x2 + 0.025x -0.494
2. The following table shows the temperature outside and the number of children who come down with colds in a major city. For the data below, select the best model.
Degree F 70 60 50 40 30 20
Number of Children 370 391 412 433 454 475
a. -2.1x + 517
b. X2 -2.1x + 517
c. 526.984 . (0.005x)
d. 2.6x3 -x2 + x-1
3.The following data shows the year and the cost (in millions of dollars) a growing company incurrs. Find the best model for the data below, letting x be years since 1991.
Year 1991 1992 1993 1994 1995 1996
Cost 6.54 13.145 26.422 53.109 106.75 214.56
a. y = 11.92x2 - 21.09x + 13.56
b. 2.58x3 -7.39 x2 + 14.19x + 5.84
c. 6.54 . (2.01x)
d. 2.1x -2
4. The following data shows the increasing payroll in thousands of dollars per month of the an airline company and the fluctuating numbers of passengers in thousands per month the company has in a given year. Find the best model for the data.
Payroll 15 20 24 26 30 32 36 38
Passengers 21 23 25 24 21 18 22 25
a. y = 0.001 x2 -0.056x + 23.005
b. y = 22.285 . (.999957x)
c. y = 0.005x + 22.24
d. y = 0.006x3 - 0.503x2 = 12.644x - 77.431
5. In Gothem City, the table below shows the mean age of a man who gets married for the first time. Find the model for the data. Let x be years since 1970.
Year 1970 1980 1990 2000
Age of Men 20.3 20.8 22 23.9
a. y= 0.0035 x2 + 0.015x + 20.3
b. y = x3 + 0.0035x2 + 0.015x +20.3
c. y = 0.12x + 19.20
d. y = 20 . (1.005x)
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Solution Summary
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Please see the attached file and check the solution especially question #4. I think there is something wrong with the choices.
1. The following gives the price in dollars of a round trip ticket from Phoenix to Portland, and the corresponding profit, in millions of dollars, for each price. For the data below, select the best model.
Price (dollars) 200 250 300 350 400 450
3.09 3.51 3.75 3.81 3.71 3.36
a. y= -3.721 x2 + 0.025 x -0.494
b. y = 0.0011x + 3.165
c. y = -2.148 x 10-8 x3 -1.627 x 10-5 x2 + 0.019x + 0.155
d. y = -3.721 x 10-5 x2 + 0.025x -0.494
Solution
First, plotting the profit vs. Price:
The curve appears to be always convex. Then, our choice is quadratic function which can be (a) or (d).
In case of (a), given price=200, profit is -148835.5.
In case of (d), given price=200, profit is 3.0176.
Thus, (d) is the best model.
...
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