Mathematical Modeling

Jonas Hall is Head of Mathematics at Rodengymnasiet in Norrtalje, Sweden, where he teaches mathematics and physics. His research interests include problem solving, the aesthetics of mathematics, and teaching with technology. He is a multiple finalist in Kappa, which is a competition for mathematics teachers in Sweden offered by the University of Stockholm. Thomas Lingefjard, PhD, is Associate Professor of Mathematics Education in the Department of Education at the University of Gothenburg. The author of more than 25 articles and 10 chapter contributions, Dr. Lingefjard's research interests include mathematical modeling and advanced mathematical thinking.

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 5.25 Measuring Sticks, 234 5.26 The Lecture Hall, 234 5.27 Progressive Braking Distances, 234 5.28 Cylinder in a Cone, 235 6 Using Differential Equations 236 6.1 Cooling III, 237 6.2 Moose Hunting, 241 6.3 The Water Container, 247 6.4 Skydiving, 250 6.5 Flu Epidemics, 256 6.6 USA's Population, 263 6.7 Predators and Prey, 274 6.8 Smoke, 285 6.9 Alcohol Consumption, 289 6.10 Who Killed the Mathematics Teacher, 292 6.11 River Clams, 297 6.12 Contamination, 297 6.13 Damped Oscillation, 297 6.14 The Potassium-Argon Method, 298 6.15 Barium, Lanthanum, and Cerium, 298 6.16 Iodine, 298 6.17 Endemic Epidemics, 299 6.18 War, 299 6.19 Farmers, Bandits, and Rulers, 299 6.20 Epidemics Without Immunity, 300 6.21 Zombie Apocalypse I, 300 6.22 Zombie Apocalypse II, 300 7 Geometrical Models 301 7.1 The Looping Pen, 302 7.2 Comparing Areas, 304 7.3 Crossing Lines, 307 7.4 Points in a Triangle, 310 7.5 Trisected Area, 316 7.6 Spirograph, 320 7.7 Connected LP Players, 326 7.8 Folding Paper, 332 7.9 The Locomotive, 336 7.10 Maximum Volume, 340 7.11 Pascal's Sn