7. For logistic modeling of an animal population in a limited environment situation, we have data...

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7. For logistic modeling of an animal population in a limited environment situation, we have data for the birth rate, Bo = 0.1 month ¹; the death rate, So = 0.05 month¹, and a population- dependent, decreasing birth rate function that is proportional to the population size according to B₁ = 0.0001 (animals * month)-¹. • What is the time-dependent differential equation for this population? • What is the value of the critical point for this population? • Show that this critical point is stable. If the initial population is Po = 200 animals, how many months does it take for this population to grow by 200 more animals? • If the initial population is Po= 800 animals, can we expect this population to grow by 200 more animals? If yes, how long will it take? If no, then explain why not. 7. For logistic modeling of an animal population in a limited environment situation, we have data for the birth rate, Bo = 0.1 month ¹; the death rate, So = 0.05 month¹, and a population- dependent, decreasing birth rate function that is proportional to the population size according to B₁ = 0.0001 (animals * month)-¹. • What is the time-dependent differential equation for this population? • What is the value of the critical point for this population? • Show that this critical point is stable. If the initial population is Po = 200 animals, how many months does it take for this population to grow by 200 more animals? • If the initial population is Po= 800 animals, can we expect this population to grow by 200 more animals? If yes, how long will it take? If no, then explain why not.

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TimeDependent Differential Equation dPdt Bo 8P 1P2 Critical Point P Bo21 01200001 500 Stability ... View the full answer