There is considerable evidence to support the theory that for some species there is a minimum population msuch that the species will become extinct if the size of the population falls below m. This condition can be incorporatedinto the logistic equation by introducing the factor (1 – m/P). Thus the modified logistic model is given by thedifferential equation" - (1-)(-)dP= kPdtPmwhere k is a constant and K is the carrying capacity.Suppose that the carrying capacity K = 10000, the minimum population m = 500, and the constant k = 0.05.Answer the following questions.1. Assuming P > O 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):

Name: There is considerable evidence to support the theory that for some sp
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Description: There is considerable evidence to support the theory that for some species there is a minimum population msuch that the species will become extinct if the size of the population falls below m. This condition can be incorporatedinto the logistic equa

Given fiffrential equation is, dPdt=kp1-PK1-mP Substituting k=0.05, K=10000 and m=500 into the given…

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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 * - ur (1-)(1-) dP kP dt where k is a constant and K is the carrying capacity. Suppose that the carrying capacity K = 10000, the minimum population m = 500, and the constant k = 0.05. Answer the following questions. 1. Assuming P > 0 for what values of P is the population increasing. Answer (in interval notation): 2. Assuming P 2 0 for what values of P is the population decreasing. Answer (in interval notation):