MHR • Advanced Functions 12 Solutions 660

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Chapter 7 Section 5 Making Connections: Mathematical Modelling With Exponential and Logarithmic Equations Chapter 7 Section 5 Question 1 Page 404 P = 1006(1.016) t 6500 = 1006(1.016) t 6500 1006 = 1.016t ! log 6500 $ " # 1006 % & = t log1.016 ! log 6500 $ " # 1006 % & t = log1.016 t &= 117.5 1920 + 117.5 = 2037.5 The off-ramp should be built in approximately June of 2037. Chapter 7 Section 5 Question 2 Page 404 1920 – 145.4 &= 1774.6 In approximately the year 1774 the town’s population was only 100. MHR • Advanced Functions 12 Solutions 721
Chapter 7 Section 5 Question 3 Page 404 a) i) P = 1006(1.016) t P = 1006(1.016) 100 &= 4920 The town’s population will be approximately 4920 in 100 years from 1920. P = 1000 ! 2 t 43.5 100 P = 1000 ! 2 43.5 &= 4921 The town’s population will be approximately 4921 in 100 years from 1920. ii) P = 1006(1.016) t 20 000 = 1006(1.016) t 20 000 1006 = 1.016t ! 20 000$ log " # 1006 % & = t log1.016 ! 20 000$ log " # 1006 % & t = log1.016 t &= 188.4 It will take approximately 188.4 years for the town’s population to reach 20 000. P = 1000 ! 2 20 000 = 1000 ! 2 20 = 2 t 43.5 log 20 = log 2 t 43.5 t 43.5 t 43.5 log 20 = t 43.5 log 2 t log 20 = 43.5 log 2 t = 43.5log 20 log 2 t &= 188 It will take approximately 188 years for the town’s population to reach 20 000. b) Answers may vary. A sample solution is shown. Quite close. The differences are due to rounding in each method. MHR • Advanced Functions 12 Solutions 722
Page 1 and 2:
Chapter 7 Tools and Strategies for
Page 3 and 4:
c) x 2 + x !1 = 0 x = !1± 12 ! 4(1
Page 5 and 6:
Chapter 7 Prerequisite Skills Quest
Page 7 and 8:
Chapter 7 Section 1 Question 4 Page
Page 9 and 10:
) c) d) Chapter 7 Section 1 Questio
Page 11 and 12: Chapter 7 Section 1 Question 10 Pag
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 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 61: Chapter 7 Section 4 Question 16 Pag
Page 65 and 66: ) i) y &= 4.21x - 3.07 ii) y &= 0.8
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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