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C-12 Appendix C PROJECT Wind Power The relatively recent [in terms of human history] transition to coal that began in Europe in the seventeenth century marked a major shift to dependence on a finite stock of fossilized fuels whose remaining energy is now equivalent to less than 11 days of sunshine. From a millennial perspective, today’s hydrocarbonbased civilization is but a brief interlude in human history. —Christopher Flavin and Seth Dunn, “Reinventing the Energy System” in Vital Signs, 1999, Lester R. Brown et al. (New York: W. W. Norton & Co., 1999) As the world’s nonrenewable energy resources such as oil and coal start to become more scarce, alternative sources such as wind and solar become increasingly important. In this project you’ll calculate some estimates concerning wind power, an industry and technology that has grown rapidly over the past two decades. (Later, in Chapter 5,* after studying exponential and logarithmic functions, we’ll be able to make some rough estimates for possible depletion dates regarding resources such as oil and coal.) In working this project, you’ll be reviewing math from the following sections of this book: • 1.3 Solving Equations • 1.6 Equations of Lines • 2.3 Inequalities • 2.4 More on Inequalities y Wind turbines in Altamont, California. (Photo by Glen Allison, PhotoDisc.) Energy (megawatts) (13, 9600) (0, 1020) t Year (t=0 corresponds to 1985) World wind-energy generating capacity, 1985 (t 0) and 1998 (t 13). Source: Data from BTM Consult, published in Vital Signs, 1999, p. 53, Lester R. Brown et al. (New York: W. W. Norton & Co., 1999) *Section and Chapter references refer to Precalculus: A Problems-Oriented Approach, 7th edition
Appendix C C-13 (a) The two data points in the previous figure show world wind-energy generating capacity for the years 1985 and 1998. What is the slope of the line joining the two points? What are the units for the slope? (b) Find the equation of the line joining the two given points. Write the answer in the form y mt b. (c) Use the result in part (b) to estimate the years in which world wind-energy generating capacity was between 3000 megawatts and 7500 megawatts (inclusive). Hint: You need to solve the inequality 3000 y 7500; round the answers to the nearest integers. (d) Your estimates in part (c) are based on the assumption that world wind-energy generating capacity increased in a straight-line fashion from 1985 to 1998. By using techniques from statistics (and more detailed data), it can be shown that a more accurate summary of world wind-energy generating capacity over these years is given by the equation (e) (f) y 6.977t 3 64.786t 2 325.4t 1012 where again, t 0 corresponds to 1985. Using this expression for y, estimate the years in which world wind-energy generating capacity was between 3000 megawatts and 7500 megawatts (inclusive). (Round the key numbers to the nearest integers.) Compare your results to those in part (c). Although increasing rapidly, wind-energy generation is currently but a small portion of the world energy picture. For instance, whereas world wind-energy generating capacity in 1998 was 9600 megawatts, the corresponding figure for nuclear energy in 1998 was 343,000 megawatts. When might wind-energy reach this level? Use the equation in part (d) to obtain one possible answer to this question. Round your answer to the nearest five years. Hint: In an appropriate viewing rectangle, you want to look for the point where the curve y 6.977t 3 64.786t 2 325.4t 1012 meets the horizontal line y 343,000. Rework part (e), but instead of using the cubic equation from part (d), use the straight-line equation obtained in part (b). Compare the results; which scenario do you think is more realistic?
Page 1 and 2: APPENDIX C Title and Page Number Pr
Page 3 and 4: Appendix C C-3 MINI PROJECT Discuss
Page 5 and 6: Appendix C C-5 MINI PROJECT Thinkin
Page 7 and 8: Appendix C C-7 1. equilateral trian
Page 9 and 10: Appendix C C-9 MINI PROJECT Flying
Page 11: Appendix C C-11 MINI PROJECT An Ine
Page 15 and 16: Appendix C C-15 and http://www.svob
Page 17 and 18: Appendix C C-17 For Figure D we can
Page 19 and 20: Appendix C C-19 MINI PROJECT A Grap
Page 21 and 22: Appendix C C-21 MINI PROJECT Who Ar
Page 23 and 24: Appendix C C-23 MINI PROJECT 1 How
Page 25 and 26: Appendix C C-25 either the quadrati
Page 27 and 28: Appendix C C-27 PROJECT The Least-S
Page 29 and 30: Appendix C C-29 Then, for any line
Page 31 and 32: Appendix C C-31 PROJECT Finding Som
Page 33 and 34: Appendix C C-33 3. When a person co
Page 35 and 36: Appendix C C-35 2. Use part (b) of
Page 37 and 38: Appendix C C-37 PROJECT Coffee Temp
Page 39 and 40: Appendix C C-39 MINI PROJECT More C
Page 41 and 42: Appendix C C-41 The calculations co
Page 43 and 44: Appendix C C-43 PROJECT Transits of
Page 45 and 46: Appendix C C-45 E A ¨ V ¨ Bª d S
Page 47 and 48: Appendix C C-47 PROJECT A Linear Ap
Page 49 and 50: Appendix C C-49 Continuing with the
Page 51 and 52: Appendix C C-51 PROJECT Constructin
Page 53 and 54: Appendix C C-53 1 y Figure A A grap
Page 55 and 56: Appendix C C-55 PROJECT Fourier Ser
Page 57 and 58: Appendix C C-57 sine and cosine fun
Page 59 and 60: Appendix C C-59 PROJECT The Motion
Page 61 and 62: Appendix C C-61 PROJECT The Design
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Appendix C C-63 denote the angles o
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Appendix C C-65 inverse trigonometr
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Appendix C C-67 PROJECT Inverse Sec
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Appendix C C-69 Alternatively, usin
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Appendix C C-71 PROJECT Snell’s L
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Appendix C C-73 vertically downward
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0 0 0 Appendix C C-75 PROJECT Vecto
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Appendix C C-77 Exercise 8 We outli
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Appendix C C-79 y y=2x+5 Îy=2 A (1
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 Appendi
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Appendix C C-83 PROJECT Parameteriz
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Appendix C C-85 It is worth noting
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Appendix C C-87 6. Show that the li
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Appendix C C-89 2. An altitude of a
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Appendix C C-91 PROJECT The Leontie
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Appendix C C-93 n x units of that
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Appendix C C-95 him/herself through
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Appendix C C-97 PROJECT The Leontie
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Appendix C C-99 As in the solution
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Appendix C C-101 MINI PROJECT 2 Con
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Appendix C C-103 PROJECT Using Hype
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Appendix C C-105 PROJECT Two Method
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Appendix C C-107 (b) Use Method 1 t
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Appendix C C-109 MINI PROJECT An Un
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Appendix C C-111 PROJECT More on Su
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Appendix C C-113 SOLUTION 25 25 a (
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Appendix C C-115 4. Simplify the fo
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