x y First Differences 3 15 Second Differences Chapter 5 Answers

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1 Chapter 5 Answers Get Set, pages a) none of these b) always decreasing c) always increasing d) constant 2... a) s Beverage Sales Versus Temperat Temperature ( C T Xmin = 0, Xmax = 7, Xscl =, Ymin = 0, Ymax = 220, Yscl = 22 b) y = 0.78x a) 9.9 ml b) 65.6 ml c) after approximately 6.5 h 6. a) $670 b) $ Linear Models, pages 8 85 Warm-Up. a) 7 b) 2 FFCM2 Chapter 5 Practice and Homework Book Answers

2 2. a) 5x b) x 2 2x + 6y. ( 2, 5). 0.5 cm cm 2 7. right isosceles triangle 8. a) 000 b) Practise. a) linear b) non-linear c) non-linear d) linear 2. a) decreasing d) increasing. a) $9.65/h b) $06.5. a) 00 d Danika's Trip Time (h) The points form a straight line with a positive slope. b) constant c) 8 km/h 5. Answers may vary. For example: a) Gross earnings compared to hours worked. b) The volume of water in a bathtub (drain plugged, water off) compared to time. c) Fuel remaining compared to time spent travelling. 6. a) As the number of days increases, the area left to be harvested decreases by a constant amount. b) approximately 00 acres c) 92 acres d) acres/day e) Constant. Walter has 92 fewer acres to harvest after each day. f) approximately 6 days t 5.2 Quadratic Models, pages Warm-Up. a) 22 b) x 2 x a) quadratic b) linear. 28 cm Joe: E = 0.25h; Adriana: E = h 7. D 8. The lines are parallel. The first differences are 2 for both lines. FFCM2 Chapter 5 Practice and Homework Book Answers 2

3 Practise. a) quadratic b) linear 2. a) quadratic b) neither c) quadratic d) linear a) y = 2x 2 x + c) y = 0.5x 2.5x 2 d) y = 0.75x +2. No. The x-values do not change by a constant amount. 5. a) As the ticket price increases, revenue increases to a maximum then decreases. b) i) approximately $ ii) approximately $9 00 c) Increasing for ticket prices less than $5 and decreasing for ticket prices greater than $5. 6. a) A quadratic model fits the data best. Edge Length (cm) Surface Area (m 2 ) First b) increasing c) y = x 2 d) 6.65 cm 2 5. Exponential Models, pages 89 9 Warm-Up. a) 27 b) c) 25 d) 6 2. a) 2(x 2 + y) b) 7x(x 2 2x + ). a) x-intercepts: (, 0), (8, 0); y-intercept: (0, 2) b) (6, ); minimum: FFCM2 Chapter 5 Practice and Homework Book Answers

4 . 2 cm 5. mean:.06; median: 0; mode: 2, kg of the $6/kg tea; kg of the $20/kg tea 7. the axis of symmetry 2 8. y ( x ) 2 2 Practise. a) 52 grains of rice b) The number of grains doubles each time, which is like repeatedly multiplying by two. 2. a) Yes. Each term is ten times the previous term. b) No. Each term is three more than the previous term. c) Yes. Each term is double the previous term.. a) exponential b) linear a) As time increases, the value of the vehicle decreases at a decreasing rate. b) approximately $600 c) dollars/year d) Decreasing. The graph becomes less steep. FFCM2 Chapter 5 Practice and Homework Book Answers

5 5. a) Toss Dice Remaining First b) Exponential. are all approximately 0.8. c) y = 7.59(0.88) x d) dice e) Xmin = 0, Xmax =, Xscl =, Ymin = 0, Ymax = 75, Yscl = 5 5. Analyse Graphical Models, pages Warm-Up. a) 7 b) a) (x 7)(x + 5) b) 9(x + )(x + 2). x =. pentagon, octagon, decagon c) 6 FFCM2 Chapter 5 Practice and Homework Book Answers 5

6 5. Sara's Running Time t Distance (m km/h: 60 km; 00 km/h: 00 km 7. B 8. a).8 s b) 600 g D Practise. a) C b) B c) A 2. C. a) Year Town X Population Town Y Population b) Town X: P = t; Town Y: P = 000(2) x c) year 6. a) Year Option A Salary ($) Option B Salary ($) b) Option A. She will earn a higher salary with Option A until year, when the salary for Option B will be higher. Her total cumulative earnings for Option A will be greater than for Option B until year 2. FFCM2 Chapter 5 Practice and Homework Book Answers 6

7 5. a) Curtis Year Amount ($) First Linnea Year Amount ($) First b) dollars/year c) Curtis: A = 2000(.05) n ; Linnea: A = 000(.05) n A Investment Comariso 0 n Curtis Linnea Year d) The ratio increases. The amount of Linnea s investment is increasing at a faster rate. 6. Yes. Both accounts would increase at a constant rate of.05, so the ratio would remain constant. FFCM2 Chapter 5 Practice and Homework Book Answers 7

8 5.5 Select a Mathematical Model, pages Warm-Up. a) b) 7 c) a) (x + )(x ) b) (2x + ) 2. a) V A b) 2 V a) 28 students b) 9 students 6. h = 0.00d d 7. vertex 8. after 0 years Practise. a) exponential b) exponential c) quadratic 2. a) Linear. The rate of change appears to be constant and positive. b) No. There is not enough data.. a) Xmin = 0, Xmax = 20, Xscl = 2, Ymin = 0, Ymax = 850, Yscl = 50 b) Quadratic. The rate of change is increasing. c) y = x x Xmin = 0, Xmax = 20, Xscl = 2, Ymin = 0, Ymax = 850, Yscl = 50 d) x = a) b) Yes. Exponential. First and second differences are not constant but ratios are all approximately.25. c) Xmin = 0, Xmax =, Xscl = 0.2, Ymin = 0, Ymax = 5, Yscl = d) exponential FFCM2 Chapter 5 Practice and Homework Book Answers 8

9 e) y = () x 5. a) Xmin = 0, Xmax = 0, Xscl =, Ymin = 0 000, Ymax = , Yscl = 5000 b) As the year increases, the value increases; the rate appears to be increasing c) exponential Year Average Value ($) First d) linear: V = 600t , r 2 = quadratic: V = 285.7t t , r 2 = exponential: V = (.05) t, r 2 = e) Xmin = 0, Xmax = 90, Xscl = 5, Ymin = 0, Ymax = , Yscl = 5000 f) i) linear: ; quadratic: 88 9; exponential: 886 ii) linear: ; quadratic: 66 9; exponential: g) None of the models work from 90 to FFCM2 Chapter 5 Practice and Homework Book Answers 9

10 Chapter 5 Review, pages a) A b) C, E c) B, D d) km/h 2. a) b) Quadratic. differences are constant.. a) approximately 75 m b) approximately 0 s c) m/s d) Increasing from 0 s to 0 s and then decreasing.. a) Year Percent First Remaining b) Exponential. are all approximately c) y = 99.99(0.976) x d) approximately 29 years 5. a) Time Amount in Amount in (years) Account A ($) Account B ($) b) It depends on how long he is investing the money. If he is investing it for less than seven years, Account A will earn more interest. If he is investing it for seven years or more, Account B will earn more interest. FFCM2 Chapter 5 Practice and Homework Book Answers 0

11 6. a) Year Average Amount ($) First b) Answers may vary. For example: Linear. First differences are approximately equal. differences are close to zero. The r-value for the linear model is closer to than for the exponential or quadratic models. c) Answers may vary. For example: y =.97x Xmin = 0, Xmax = 6, Xscl = 2, Ymin = 0, Ymax = 0 000, Yscl = 500 d) Answers may vary. For example: i) $09. ii) $ FFCM2 Chapter 5 Practice and Homework Book Answers