Solutions 11: Fitting Linear Models to Data
Solutions to Try Its
1. [latex]54^\circ \text{F}[/latex] 2. 150.871 billion gallons; extrapolationSolutions to Odd-Numbered Exercises
1. When our model no longer applies, after some value in the domain, the model itself doesn’t hold. 3. We predict a value outside the domain and range of the data. 5. The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data. 7. 61.966 years 9. No 11. No 13. Interpolation. About [latex]60^\circ \text{ F}[/latex]. 15. C 17. B 19.
21.
23. Yes, trend appears linear because [latex]r=0.\text{985}[/latex] and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.
25. [latex]y=\text{1}.\text{64}0x+\text{13}.\text{8}00[/latex] , [latex]r=0.\text{987}[/latex]
27. [latex]y=-0.962x+26.86, r=-0.965[/latex]
29. [latex]y=-\text{1}.\text{981}x+\text{6}0.\text{197}[/latex] ; [latex]r=-0.\text{998}[/latex]
31. [latex]y=0.\text{121}x - 38.841,r=0.998[/latex]
33. [latex]\left(-2,\text{ }-6\right),\left(1,\text{ }-12\right),\left(5,\text{ }-20\right),\left(6,\text{ }-22\right),\left(9,\text{ }-28\right)[/latex]; [latex]y=-2x - 10[/latex]
35. [latex]\left(\text{189}.\text{8},0\right)[/latex] If 18,980 units are sold, the company will have a profit of zero dollars.
37. [latex]y=0.00587x+\text{1985}.4\text{1}[/latex]
39. [latex]y=\text{2}0.\text{25}x-\text{671}.\text{5}[/latex]
41. [latex]y=-\text{1}0.\text{75}x+\text{742}.\text{5}0[/latex]
43. Yes
45. Increasing
47. [latex]y=-\text{3}x+\text{26}[/latex]
49. 3
51. [latex]y=\text{2}x-\text{2}[/latex]
53. Not linear
55. parallel
57. [latex]\left(-9,0\right);\left(0,-7\right)[/latex]
59. Line 1: [latex]m=-2[/latex]; Line 2: [latex]m=-2[/latex]; Parallel
61. [latex]y=-0.2x+21[/latex]
63.
65. 250
67. 118,000
69. [latex]y=-\text{3}00x+\text{11},\text{5}00[/latex]
71. a) 800 b) 100 students per year c) [latex]P\left(t\right)=100t+1700[/latex]
73. 18,500
75. $91,625
77. Extrapolation.
79.
81. Midway through 2024
83. [latex]y=-1.294x+49.412;\text{ } r=-0.974[/latex]
85. Early in 2022
87. 7,660Licenses & Attributions
CC licensed content, Shared previously
- Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected]..
