Your mum is an avid whale watcher and she is concerned about her blubbery friends. As...

 

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Your mum is an avid whale watcher and she is concerned about her blubbery friends. As a first year Mathematical Modelling student, you tell her that you got this! You consider the problem of the survival of the whale population and that if the number of whales falls below a minimum survival level m, the species will become extinct. You assume also that the population is limited by the carrying capacity M of the environment. You and your buddies come up with the following model for the whale population: dP k(M - P)(P-m), dt where P(t) denotes the whale population at time t and k is a positive constant. 1. Discuss the following model for the whale population by problematizing it in terms ofits key parameters m, M, and Po. (6] 2. Solve your model above assuming that m< P< M for all time. 18] 3. What happens if the whale population grows infinitely large? 14] 4. Discuss how you would test the validity of your model. 14] 5. Assuming that the model reasonably estimates the whale population, what implications are suggested for fishing? What controls would you suggest? [4] Your mum is an avid whale watcher and she is concerned about her blubbery friends. As a first year Mathematical Modelling student, you tell her that you got this! You consider the problem of the survival of the whale population and that if the number of whales falls below a minimum survival level m, the species will become extinct. You assume also that the population is limited by the carrying capacity M of the environment. You and your buddies come up with the following model for the whale population: dP k(M - P)(P-m), dt where P(t) denotes the whale population at time t and k is a positive constant. 1. Discuss the following model for the whale population by problematizing it in terms ofits key parameters m, M, and Po. (6] 2. Solve your model above assuming that m< P< M for all time. 18] 3. What happens if the whale population grows infinitely large? 14] 4. Discuss how you would test the validity of your model. 14] 5. Assuming that the model reasonably estimates the whale population, what implications are suggested for fishing? What controls would you suggest? [4]

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dp we have mePLM hnce Positiva so MP is positive t pmis dp Ldt MP Pm M... View the full answer