Differential equations help?

Posted on 2016-03-11 18:33:00 in Math by BREN

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=10000, the minimum population m=1000, and the constant k=0.15. Answer the following questions. 
Assuming P≥0 for what values of P is the population increasing. 
Assuming P≥0 for what values of P is the population decreasing.

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