1.9 Projects assume that growth rates are constant from year to year (complications will come later). For now consider each growth rate as representing a different region in Florida. 1. Construct a spreadsheet (or other simulation) tracking three bobcat populations, each initially consisting of 100 individuals, over a period of 10 years under the three types of environmental conditions. Plot all three simulations on a single graph. The graph she 8 with the current year), it should have a legend uch, and the style should have each curve identifiable when have dates on the horizontal axis (starting with the current year), it sh identifying which curve is which, and the style should have a printed in black ink. then you A blood printed in all 2. Repeat part 1 over a period of 25 years. You should have noticed that under the best conditions the population is growing. Several management plans have been discussed. The first is to allow one bobcat per vear to be hunted. The second is to allow five bobcats per year to be hunted. The third is to allow one percent of the animals to be hunted. The last is to let five percent of the animals be hunted. Construct a simulation which compares these strategies over 10 and 25 years. Which of these strategies result in a stable population? imant to find strategies which cause the Alcohol cod Project Com 2. Repeat part 1 over 2 0 3. You should have noticed that under the be is to allow one bobcat per year TABLE 1.1 Gresik then you iced that under the best conditions the population is grow at plans have been discussed. The first is to allow one bobcat econd is to allow five bobcats per year to be hunted. The third i st of the animals to be hunted. The last is to let five percent of the he hunted. Construct a simulation which compares these strategies over 10 and 25 years. Which of these strategies result in a stable population? 4. Continuing with the theme of part 3, experiment to find strategies which cause the population to stabilize. Find a strategy (which can be more involved than just subtracting a fixed number or percentage) which causes the population to rise to 200 animals (give! or take an animal or two) and then stabilize. A blood cele concentart Alcohol contes Project Cher ure 1.26 Thaile a cimulation which compat wus s uver II f 10 and then you to allow one percell UI LI animals be hunted. Construct a simulation whic 25 years. Which of these strategies result in a stable population to find strategies which cause the A blood cil Alcohol cute 4. Continuing with the theme of part 3, experiment to find strategies wh ulation to stabilize. Find a strategy (which can be more involved than just so fixed number or percentage) which causes the population to rise to 200 animal or take an animal or two) and then stabilize. Project Cars ure 1.26. The or periun qua minute. (Tetra short time 1. As padkober 5. You should also have noticed that under the worst conditions the population is declining. Proposed management plans include adding three animals per year, adding 10 animals per year, adding one percent of the population each year, and adding five percent of the population each year. Compare these strategies for 10 and 25 years. Which strategies cause the population to stabilize? 6. Experiment to find strategies which will cause the population under the wors conditions to stabilize at 50 and at 200 animals. 7. Which of the strategies in parts 3 and 5 are affine? By hand, analyze these equations, which are affine) to find fixed points and test for stability. Use the theory of alus equations to verify the numerical results. the scals Project 1.3. Blood Alcohol Model and Assumptions: (Data are from Davis. Porta, Uhl, Calculus & Mathem ves14 1994 Addison Wesley Longman Inc. Reprinted by Permissi iculus & Mathematica: Addison Wesley Longman.) The average human body climiny ms of An average college of fluid in his hour. has about ahou Project 1.3. Blood Alcohol Model Data and Assumptions: (Data are from Davis, Porta, Uhl, Calculus&Moth Derivatives[14] 1994 Addison Wesley Longman Inc. Reprinted by Permission Addison Wesley Longman.) The average human body eliminates 12 grams of alcohol per hour. An average college age male in good shape weighing K kilograms has about .68K liters of fluid in his body. A college-age female in good shape weighing K kilograms has about .65K liters of fluid in her body. People in poor shape have less. One kilogram = 2.2046 pounds. Threshold for legal driving: If your body fluids contain more than one gram of alcohol per liter of body fluids (or 0.1 gm/100 ml which is the usual way of reporting it), 1 Discrete Dynamical Systems Type of Drink Grams of Alcohol 12 ounce regular beer 12 ounce light beer 4 ounce port wine 4 ounce burgundy wine 4 ounce rose wine 1.5 ounce 100-proof vodka 1.5 ounce 100-proof bourbon 1.5 ounce 80-proof vodka 1.5 ounce 80-proof bourbon 13.6 11.3 16.4 10.9 10.0 16.7 16.7 13.4 13.4 TABLE 1.1 Grams of Alcohol for Different Types of Drinks. then you are too drunk to drive legally in most states. Find out the level for your state and use it in this project. A blood alcohol concentration of 4.0 gm/l is likely to result in coma. A blood alcohol concentration of 4.5-5.0 gm/l is likely to result in death. Alcohol content of various beverages: see Table 1.1 Project: Construct the basic model from the compartmental diagram shown in Fig. ure 1.26. This diagram was drawn using Stella; recall that circles either hold parameters or perform operations on parameters. Pick an appropriate time step. We suggest one minute. (Technically this is a continuous model, but we are treating it as discrete with a short time step.) Pick a hypothetical weight and sex. 1. Assume your hypothetical person arrives at a party and instantaneously downs a six- pack of beer (i.e., high initially alcohol level, no input flow). Graph alcohol concentration as a function of time. Plot the legal driving level on the same graph. Be very careful of the scales. How long will it be before Hypothetical can drive home legally? 11 anal Grams 1.9 Projects assume that growth rates are constant from year to year (complications will come later). For now consider each growth rate as representing a different region in Florida. 1. Construct a spreadsheet (or other simulation) tracking three bobcat populations, each initially consisting of 100 individuals, over a period of 10 years under the three types of environmental conditions. Plot all three simulations on a single graph. The graph she 8 with the current year), it should have a legend uch, and the style should have each curve identifiable when have dates on the horizontal axis (starting with the current year), it sh identifying which curve is which, and the style should have a printed in black ink. then you A blood printed in all 2. Repeat part 1 over a period of 25 years. You should have noticed that under the best conditions the population is growing. Several management plans have been discussed. The first is to allow one bobcat per vear to be hunted. The second is to allow five bobcats per year to be hunted. The third is to allow one percent of the animals to be hunted. The last is to let five percent of the animals be hunted. Construct a simulation which compares these strategies over 10 and 25 years. Which of these strategies result in a stable population? imant to find strategies which cause the Alcohol cod Project Com 2. Repeat part 1 over 2 0 3. You should have noticed that under the be is to allow one bobcat per year TABLE 1.1 Gresik then you iced that under the best conditions the population is grow at plans have been discussed. The first is to allow one bobcat econd is to allow five bobcats per year to be hunted. The third i st of the animals to be hunted. The last is to let five percent of the he hunted. Construct a simulation which compares these strategies over 10 and 25 years. Which of these strategies result in a stable population? 4. Continuing with the theme of part 3, experiment to find strategies which cause the population to stabilize. Find a strategy (which can be more involved than just subtracting a fixed number or percentage) which causes the population to rise to 200 animals (give! or take an animal or two) and then stabilize. A blood cele concentart Alcohol contes Project Cher ure 1.26 Thaile a cimulation which compat wus s uver II f 10 and then you to allow one percell UI LI animals be hunted. Construct a simulation whic 25 years. Which of these strategies result in a stable population to find strategies which cause the A blood cil Alcohol cute 4. Continuing with the theme of part 3, experiment to find strategies wh ulation to stabilize. Find a strategy (which can be more involved than just so fixed number or percentage) which causes the population to rise to 200 animal or take an animal or two) and then stabilize. Project Cars ure 1.26. The or periun qua minute. (Tetra short time 1. As padkober 5. You should also have noticed that under the worst conditions the population is declining. Proposed management plans include adding three animals per year, adding 10 animals per year, adding one percent of the population each year, and adding five percent of the population each year. Compare these strategies for 10 and 25 years. Which strategies cause the population to stabilize? 6. Experiment to find strategies which will cause the population under the wors conditions to stabilize at 50 and at 200 animals. 7. Which of the strategies in parts 3 and 5 are affine? By hand, analyze these equations, which are affine) to find fixed points and test for stability. Use the theory of alus equations to verify the numerical results. the scals Project 1.3. Blood Alcohol Model and Assumptions: (Data are from Davis. Porta, Uhl, Calculus & Mathem ves14 1994 Addison Wesley Longman Inc. Reprinted by Permissi iculus & Mathematica: Addison Wesley Longman.) The average human body climiny ms of An average college of fluid in his hour. has about ahou Project 1.3. Blood Alcohol Model Data and Assumptions: (Data are from Davis, Porta, Uhl, Calculus&Moth Derivatives[14] 1994 Addison Wesley Longman Inc. Reprinted by Permission Addison Wesley Longman.) The average human body eliminates 12 grams of alcohol per hour. An average college age male in good shape weighing K kilograms has about .68K liters of fluid in his body. A college-age female in good shape weighing K kilograms has about .65K liters of fluid in her body. People in poor shape have less. One kilogram = 2.2046 pounds. Threshold for legal driving: If your body fluids contain more than one gram of alcohol per liter of body fluids (or 0.1 gm/100 ml which is the usual way of reporting it), 1 Discrete Dynamical Systems Type of Drink Grams of Alcohol 12 ounce regular beer 12 ounce light beer 4 ounce port wine 4 ounce burgundy wine 4 ounce rose wine 1.5 ounce 100-proof vodka 1.5 ounce 100-proof bourbon 1.5 ounce 80-proof vodka 1.5 ounce 80-proof bourbon 13.6 11.3 16.4 10.9 10.0 16.7 16.7 13.4 13.4 TABLE 1.1 Grams of Alcohol for Different Types of Drinks. then you are too drunk to drive legally in most states. Find out the level for your state and use it in this project. A blood alcohol concentration of 4.0 gm/l is likely to result in coma. A blood alcohol concentration of 4.5-5.0 gm/l is likely to result in death. Alcohol content of various beverages: see Table 1.1 Project: Construct the basic model from the compartmental diagram shown in Fig. ure 1.26. This diagram was drawn using Stella; recall that circles either hold parameters or perform operations on parameters. Pick an appropriate time step. We suggest one minute. (Technically this is a continuous model, but we are treating it as discrete with a short time step.) Pick a hypothetical weight and sex. 1. Assume your hypothetical person arrives at a party and instantaneously downs a six- pack of beer (i.e., high initially alcohol level, no input flow). Graph alcohol concentration as a function of time. Plot the legal driving level on the same graph. Be very careful of the scales. How long will it be before Hypothetical can drive home legally? 11 anal Grams