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10, 000, draw a direction field and use For the case where k = 1, M = 100, 000 and m = it to sketch several solutions for various initial populations. What are the equilibrium solutions? One can show that k(М-т), M(Po – m)e (Ро — т)е t. т(Ро — М) M P(t) = k(М-т) t M – (Po – M) is a solution with initial population P(0) = Po. Use this to show that, if P(0) < m, then there is a time t at which P(t) = 0 (and so the population will be extinct).

10, 000, draw a direction field and use For the case where k = 1, M = 100, 000 and m = it to sketch several solutions for various initial populations. What are the equilibrium solutions? One can show that k(М-т), M(Po – m)e (Ро — т)е t. т(Ро — М) M P(t) = k(М-т) t M – (Po – M) is a solution with initial population P(0) = Po. Use this to show that, if P(0) < m, then there is a time t at which P(t) = 0 (and so the population will be extinct).

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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A population of fish is living in an environment with limited resources. This environment can only support the population if it contains no more than M fish (otherwise some fish would starve due to an inadequate supply of food, etc.). There is considerable evidence to support the theory that, for some fish species, there is a minimum population m such that the species will become extinct if the size of the population falls below m. Such a population can be modelled using a modified logistic equation: dP =(1-)(-) m dt M
Transcribed Image Text:A population of fish is living in an environment with limited resources. This environment can only support the population if it contains no more than M fish (otherwise some fish would starve due to an inadequate supply of food, etc.). There is considerable evidence to support the theory that, for some fish species, there is a minimum population m such that the species will become extinct if the size of the population falls below m. Such a population can be modelled using a modified logistic equation: dP =(1-)(-) m dt M
10, 000, draw a direction field and use For the case where k = 1, M = 100, 000 and m = it to sketch several solutions for various initial populations. What are the equilibrium solutions? One can show that k(М-т), M(Po – m)e (Ро — т)е t. т(Ро — М) M P(t) = k(М-т) t M – (Po – M) is a solution with initial population P(0) = Po. Use this to show that, if P(0) < m, then there is a time t at which P(t) = 0 (and so the population will be extinct).
Transcribed Image Text:10, 000, draw a direction field and use For the case where k = 1, M = 100, 000 and m = it to sketch several solutions for various initial populations. What are the equilibrium solutions? One can show that k(М-т), M(Po – m)e (Ро — т)е t. т(Ро — М) M P(t) = k(М-т) t M – (Po – M) is a solution with initial population P(0) = Po. Use this to show that, if P(0) < m, then there is a time t at which P(t) = 0 (and so the population will be extinct).
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