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Mathematics, 19.06.2020 13:57 REAPR9043
There is considerable evidence to support the theory that for some species there is a minimum population m such that the species will become extinct if the size of the population falls below m. This condition can be incorporated into the logistic equation by introducing the factor (1−m/P). Thus the modified logistic model is given by the differential equation
dPdt=kP(1−PK)(1−mP)
where k is a constant and K is the carrying capacity.
Suppose that the carrying capacity K=40000, the minimum population m=900, and the constant k=0.1. Answer the following questions.
1. Assuming P≥0 for what values of P is the population increasing. Answer (in interval notation):
2. Assuming P≥0 for what values of P is the population decreasing. Answer (in interval notation):
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