1. Exercise B.1 Guessing China's population a. The book land of 500 million: A Geography of China was published in 1955. Suppose the opening paragraph says China's population had been growing in an exponential fashion at 3.5%/yr. And suppose this rate of growth were to have continued to the year 1995. What is your guess for the population in 1995? 2. Exercise B.2 Toxic decay a. A train wreck in 1997 leads to a spill of 480 tons of the chemical XYZ, which becomes absorbed in the soil. Experts are called to the scene. They announce that the chemical will degrade with a half-life of 20 years, and they say there will be no danger once the amount of chemical in the soil falls below 30 tons. In what year will the soil be safe? 3. Exercise B.3 Doubling times for large animals a. Pratt (1995, 58) summarizes the range of biotic potentials for four broad classes of animals. The biotic potential is defined as the rate of exponential growth expected when the animal is free to grow without constraints from the environment. For large mammals, the biotic potential can range from a low of 2%/yr to a high of 50%/yr. What is the corresponding range of doubling times? 4. Exercise B.4 Doubling time in days a. Pratt reports that biotic potentials for small mammals can be as high as 800%/yr. The 800%/yr growth rate suggests that years is not an appropriate time for simulating this population. Change the growth rate to %/day and give the doubling time in days. 5. Exercise B.5 Reach $1 million a. You open a savings account on the day your child is born. The bank guarantees that the balance in the account will grow exponentially at 10%/yr forever. Your goal is to have $1 million in the account by the time your child reaches 70 years of age, and you plan no further deposits. How much do you deposit in the account? 6. Exercise B.6 Advice for the king a. D. H. Meadows et al. (1972, 29) describe a Persian legend about a clever courtier who presented a beautiful chessboard to his king. The courtier asked the king to show his favor by simply giving the courtier 1 grain of rice for the first square on the board. He would then follow that with 2 grains for the second square, 4 grains for the third, and so on. Suppose the king turns to you for advice. He tells you that the kingdom's entire storage of 1 million tons is available. You count 64 squares on a chessboard, and you know there are 5,760 grains in a pound and 2,000 pounds in a ton. Does the king have enough rice to accept the chessboard? 7. B.7 Rice weevil optimum a. Odum (1971, 182) describes the doubling time for the rice weevil at just under 1 week, provided the temperature is near the optimum value. Assume there are no limits on growth and the weevil population doubles in 1 week. How long will it take for the weevils to increase by a millionfold? 8. B. 8 Rice weevils feel the heat a. Odum reports a doubling time of 5.78 weeks if the temperature is 4.5 degree C above the optimum. How long will it take for the weevils to increase by a millionfold under these conditions? Modeling the Environment (An Introduction to Systems Dynamics Modeling of Environmental Systems) by Andrew Ford http://www.islandpress.org/ford