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. Th 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 dP dt =kP where k is a constant and K is the carrying capacity. Suppose that the carrying capacity K = 20000, the minimum population m = 500, and the constant k = 0.2. 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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A): What is the carrying capacity of the population? B): What is the total population at the moment the population is growing at the fastest rate?    Please find part A and B