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 $$\frac{dP}{dt} = k P \left(1-\frac{P}{K}\right)\left(1-\frac{m}{P}\right)$$ where $k$ is a constant and $K$ is the carrying capacity.

Suppose that the carrying capacity $K = 10000,$ the minimum population $m = 600,$ and the constant $k = 0.05.$ Answer the following questions.

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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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