Preface xi

Introduction xiii

About the Companion Website xxx

1 Some Introductory Problems 1

1.1 Ticket Prices, 3

1.2 How Long Will the Pasture Last in a Field?, 7

1.3 A Bit of Chemistry, 10

1.4 Sydney Harbor Bridge, 16

1.5 Perspective, 19

1.6 Lake Erie's Area, 21

1.7 Zebra Crossing, 25

1.8 The Security Case, 31

1.9 Personal Measurements, 34

1.10 Height of the Body, 34

1.11 Lamp Pole, 35

1.12 The Skyscraper, 35

1.13 The Fence, 35

1.14 The Corridor, 35

1.15 Bird Feeders, 35

1.16 Golf, 36

2 Linear Models 37

2.1 Are Women Faster Than Men?, 38

2.2 Taxi Companies, 40

2.3 Crime Development, 47

2.4 The Metal Wire, 52

2.5 Options Trading, 57

2.6 Flying Foxes, 62

2.7 Knots on a Rope, 66

2.8 The Candle, 66

2.9 Hooke's Law, 66

2.10 Ranking, 67

2.11 Dolbear's Law, 67

2.12 Man at Office, 68

2.13 A Stack of Paper, 68

2.14 Milk Production in Cows, 69

3 Nonlinear Empirical Models I 70

3.1 Galaxy Rotation, 71

3.2 Olympic Pole Vaulting, 73

3.3 Kepler's Third Law, 79

3.4 Density, 83

3.5 Yeast, 87

3.6 Cooling I, 88

3.7 Modeling the Population of Ireland, 93

3.8 The Rule of 72, 96

3.9 The Fish Farm I, 100

3.10 New Orleans Temperatures, 104

3.11 The Record Mile, 107

3.12 The Rocket, 107

3.13 Stopping Distances, 107

3.14 A Bottle with Holes, 108

3.15 The Pendulum, 108

3.16 Radio Range, 108

3.17 Running 400 Meters, 108

3.18 Blue Whale, 109

3.19 Used Cars, 109

3.20 Texts, 110

4 Nonlinear Empirical Models II 111

4.1 Cooling II, 112

4.2 Body Surface Area, 116

4.3 Warm?]Blooded Animals, 120

4.4 Control of Insect Pests, 123

4.5 Selling Magazines for Christmas, 125

4.6 Tumor, 136

4.7 Free Fall, 141

4.8 Concentration, 145

4.9 Air Current, 150

4.10 Tides, 153

4.11 Fitness, 156

4.12 Life Expectancy versus Average Income, 157

4.13 Stockholm Center, 157

4.14 Workforce, 157

4.15 Population of Sweden, 158

4.16 Who Killed the Lion?, 158

4.17 AIDS in United States, 159

4.18 Thermal Comfort, 159

4.19 Watts and Lumen, 159

4.20 The Beaufort Scale, 160

4.21 The von Bertalanffy Growth Equation, 161

5 Modeling with Calculus 162

5.1 The Fish Farm II, 163

5.2 Titration, 169

5.3 The Bowl, 176

5.4 The Aircraft Wing, 180

5.5 The Gateway Arch in St. Louis, 182

5.6 Volume of a Pear, 187

5.7 Storm Flood, 190

5.8 Exercise, 193

5.9 Bicycle Reflectors, 202

5.10 Cardiac Output, 206

5.11 Medication, 210

5.12 New Song on Spotify, 215

5.13 Temperature Change, 221

5.14 Tar, 224

5.15 Bicycle Reflectors Revisited, 229

5.16 Gas Pressure, 229

5.17 Airborne Attacks, 229

5.18 Railroad Tracks, 230

5.19 Cobb-Douglas Production Functions, 230

5.20 Future Carbon Dioxide Emissions, 231

5.21 Overtaking, 232

5.22 Population Dynamics of India, 232

5.23 Drag Racing, 232

5.24 Super Eggs, 233