MHR • Advanced Functions 12 Solutions 660

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e) How old is bone that contains 10% of its original carbon-14? Solution: 0.1 = 0.999!122(0.999!875) t 0.1 log = log 0.999!875t 0.999!122 0.1 log = t log 0.999!875 0.999!122 0.1 log t = 0.999!122 log 0.999!875 t &= 18!412.5 The bone is about 5545 years old. Using the formula from the exponential regression, determine the half-life of carbon-14. Solution: t ! 1$ h " # 2% & = 0.999!875 t t ! log 1 $ h " # 2% & = log 0.999!875 t t h log ! 1 $ " # 2% & = t log 0.999!875 ! t log 1 $ " # 2% & h = t log 0.999!875 ! log 1 $ " # 2% & h = log 0.999!875 h &= 5545 The half-life is about 5545 years. MHR • Advanced Functions 12 Solutions 729
Chapter 7 Section 5 Question 13 Page 407 Answers may vary. A sample solution is shown. a), b) Data on bacteria in a petri dish over several days. Day Bacteria (thousands) 1 2.8 2 7.2 3 17.6 4 40.0 5 78.6 6 125.2 7 162.8 8 183.8 9 193.4 10 197.4 c) d) The logistic curve models the data almost perfectly. MHR • Advanced Functions 12 Solutions 730
Page 1 and 2:
Chapter 7 Tools and Strategies for
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c) x 2 + x !1 = 0 x = !1± 12 ! 4(1
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Chapter 7 Prerequisite Skills Quest
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Chapter 7 Section 1 Question 4 Page
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) c) d) Chapter 7 Section 1 Questio
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Chapter 7 Section 1 Question 10 Pag
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Page 15 and 16:
Page 17 and 18:
Chapter 7 Section 2 Techniques for
Page 19 and 20: c) Answers may vary. A sample solut
Page 21 and 22: Chapter 7 Section 2 Question 8 Page
Page 23 and 24: Chapter 7 Section 2 Question 10 Pag
Page 25 and 26: f) 4 x ! 3!18(4 ! x ) = 0 (4 x ) 2
Page 27 and 28: d) e) There is no zero so there is
Page 37 and 38: d) 2log w + 3log w + 1 2 log ! 1 $
Page 43 and 44: ) Let x = log b m and y = log b n b
Page 47 and 48: Chapter 7 Section 4 Techniques for
Page 51 and 52: Check: d) 1 = log( y + 9) ! log y "
Page 53 and 54: ! f) log p + 5 $ " # p +1% & = 3 p
Page 65 and 66: ) i) y &= 4.21x - 3.07 ii) y &= 0.8
Page 69: Chapter 7 Section 5 Question 12 Pag
Page 75 and 76: Chapter 7 Review Chapter 7 Review Q
Page 77 and 78: ! b) 0.05 = 1 $ " # 2% & t 5 log0.0
Page 79 and 80: Chapter 7 Review Question 7 Page 40
Page 81 and 82: Chapter 7 Review Question 13 Page 4
Page 83 and 84: d) i) A = 500(1.033) 2t + 500(0.01)
Page 85 and 86: Chapter 7 Practice Test Question 6
Page 87 and 88: d) Chapter 7 Practice Test Question
Page 89 and 90: Chapter 7 Practice Test Question 10
Page 91: e) i) y &= 95.67(0.96) 15 y &= 49.6
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MHR • Advanced Functions 12 Solutions 660

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