Suppose That a Population of Bacteria Grows According to the Logistic

Suppose that a population of bacteria grows according to the logistic equation $\frac { d P } { d t } = 0.01 P - 0.0002 P ^ { 2 }$ , where P is the population measured in thousands and t is time measured in days.(a) What is the carrying capacity? What is the value of k?
(b) A direction field for this equation is given below. Where are the slopes close to 0? Where are the slope values the largest? Where are the solutions increasing? Where are the solutions decreasing? (c) Use the direction field to sketch solutions for initial populations of 10, 30, 50, and 70. What do these solutions have in common? How do they differ? Which solutions have inflection points? At what population levels do they occur?
(d) What are the equilibrium solutions? How are the other solutions related to these solutions?

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(a) 50 thousand; (b) Near P = 0 or P = ...

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