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2. Concerned that the nittany mouse population will get out of control, the Pennsylvania Department of Conservation and Natural Resources (DCNR) introduces the nittany hawk (not a real species), which preys on nittany mice. DCNR estimates that the hawks will eat 500 mice per year. (a) Formulate the differential equation modeling the nittany mouse population in this new scenario. Before you proceed to part (b): Did you follow the italicized instructions at the top of the page? Does your differential equation in (a) have letters in it whose numerical values you kmow, but did not insert? If so, reurite the differential cquation, substituting those numerical values in place of the letters. Keep those numbers in place throughout the rest of your work on this problem. (b) Do a qualitative analysis of the differential equation in order to generate a solution portrait for all mathematical solutions, and another portrait for physically viable solutions. (c) Does your new model predict that the mice and hawks can co-exist? Explain. (d) Find the general solution to your differential equation. (e) Assuming the current mouse population is 1000, and your model predicts that the mouse popu- lation will grow, what will the mouse population be in fiye years? If inot extinctio

2. Concerned that the nittany mouse population will get out of control, the Pennsylvania Department of Conservation and Natural Resources (DCNR) introduces the nittany hawk (not a real species), which preys on nittany mice. DCNR estimates that the hawks will eat 500 mice per year. (a) Formulate the differential equation modeling the nittany mouse population in this new scenario. Before you proceed to part (b): Did you follow the italicized instructions at the top of the page? Does your differential equation in (a) have letters in it whose numerical values you kmow, but did not insert? If so, reurite the differential cquation, substituting those numerical values in place of the letters. Keep those numbers in place throughout the rest of your work on this problem. (b) Do a qualitative analysis of the differential equation in order to generate a solution portrait for all mathematical solutions, and another portrait for physically viable solutions. (c) Does your new model predict that the mice and hawks can co-exist? Explain. (d) Find the general solution to your differential equation. (e) Assuming the current mouse population is 1000, and your model predicts that the mouse popu- lation will grow, what will the mouse population be in fiye years? If inot extinctio

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This Is a question that we went over in class but i do not fully understand it i need number 2 but my teacher said that number 2 builds off number 1.
1. The population of the nittany mouse (not a real species) is assumed to grow by 40% each P = P(t) be the mouse population at time t, in years. year. Let (a) Formulate the differential equation modeling the nittany mouse population. Before you proceed to part (b): Did you follow the italicized instructions at the top of the page? Does your differential equation in (a) have a letter in it whose numerical value you know, but did not insert? If so, rewrite the differential equation, substituting that numerical value in place of the letter. Keep that number in place throughout the rest of your work on this problem. (b) Do a qualitative analysis of the differential equation in order to generate a solution portrait for all mathematical solutions, and another portrait for physically viable solutions. (c) Find the general solution to your differential equation. (d) Assuming the current population is 1000, what will the population be in five years? (e) How long will it take for the population to become 10,000? 2. Concerned that the nittany mouse population will get out of control, the Pennsylvania Department of Conservation and Natural Resources (DCNR) introduces the nittany hawk (not a real species), which preys on nittany mice. DCNR estimates that the hawks will eat 500 mice per year. (a) Formulate the differential equation modeling the nittany mouse population in this new scenario. Before you proceed to part (b): Did you follow the italicized instructions at the top of the page? Does your differential equation in (a) have letters in it whose numerical values you know, but did not insert? If so, reurite the differential equation, substituting those numerical values in place of the letters. Keep those numbers in place throughout the rest of your work on this problem. (b) Do a qualitative analysis of the differential equation in order to generate a solution portrait for all mathematical solutions, and another portrait for physically viable solutions. (c) Does your new model predict that the mice and hawks cam co-exist? Explain. (d) Find the general solution to your differential equation. (e) Assuming the current mouse population is 1000, and your model predicts that the mouse popu- lation will grow, what will the mouse population be in five years? If instead your model predicts extinction for the mice, how long will that take?
Transcribed Image Text:1. The population of the nittany mouse (not a real species) is assumed to grow by 40% each P = P(t) be the mouse population at time t, in years. year. Let (a) Formulate the differential equation modeling the nittany mouse population. Before you proceed to part (b): Did you follow the italicized instructions at the top of the page? Does your differential equation in (a) have a letter in it whose numerical value you know, but did not insert? If so, rewrite the differential equation, substituting that numerical value in place of the letter. Keep that number in place throughout the rest of your work on this problem. (b) Do a qualitative analysis of the differential equation in order to generate a solution portrait for all mathematical solutions, and another portrait for physically viable solutions. (c) Find the general solution to your differential equation. (d) Assuming the current population is 1000, what will the population be in five years? (e) How long will it take for the population to become 10,000? 2. Concerned that the nittany mouse population will get out of control, the Pennsylvania Department of Conservation and Natural Resources (DCNR) introduces the nittany hawk (not a real species), which preys on nittany mice. DCNR estimates that the hawks will eat 500 mice per year. (a) Formulate the differential equation modeling the nittany mouse population in this new scenario. Before you proceed to part (b): Did you follow the italicized instructions at the top of the page? Does your differential equation in (a) have letters in it whose numerical values you know, but did not insert? If so, reurite the differential equation, substituting those numerical values in place of the letters. Keep those numbers in place throughout the rest of your work on this problem. (b) Do a qualitative analysis of the differential equation in order to generate a solution portrait for all mathematical solutions, and another portrait for physically viable solutions. (c) Does your new model predict that the mice and hawks cam co-exist? Explain. (d) Find the general solution to your differential equation. (e) Assuming the current mouse population is 1000, and your model predicts that the mouse popu- lation will grow, what will the mouse population be in five years? If instead your model predicts extinction for the mice, how long will that take?
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