1. Consider a population P(t) satisfying the logistic equationdP= aP – bP2 where B = aP isdtthe time rate at which births occur and D = bP2 is the rate at which deaths occur. If initialpopulation is P(0) = Po and Bọ biths per month and Do deaths per month are occuring atBoPotime t = 0, show that the limiting population is M =Do2. A man with a parachute jumps out of a hovering helicopter at height H. During the fall, theman's drag coefficient is k (with closed parachute) and nk (with open parachute) and airreistant is taken as proportional to velocity. The total weight of the man and his parachute ism. Take the initial velocity when he jumped to be zero. Gravitatioanl constant is g. Find thebest time for the man to open his parachute after he leaves the helicopter for the quickest falland yet "soft" landing at touchdown speed < vo.FRFGFigure 1: The Jumper Model

The given logistic equation can be written as: dPdt=aP-bP2Where B=aP is the time rate at which birth…

Consider a population P(t) satisfying the logistic equation dP = aP – bP2 where B = aP is dt - the time rate at which births occur and D = bP² is the rate at which deaths occur. If initial population is P(0) = Po and B, biths per month and Do deaths per month are occuring at BoPo time t = 0, show that the limiting population is M = Do %3D

Consider a population P(t) satisfying the logistic equation dP = aP – bP2 where B = aP is dt - the time rate at which births occur and D = bP² is the rate at which deaths occur. If initial population is P(0) = Po and B, biths per month and Do deaths per month are occuring at BoPo time t = 0, show that the limiting population is M = Do %3D

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.EA: Extended Application Managing Renewable Resources

Problem 2EA

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