# 150100502040603. Suppose that a population develops according to the logisticequation(c) Use the direction field to sketch solutions for initial pop-ulations of 20, 40, 60, 80, 120, and 140. What do thesedP= 0.05P - 0.0005P2dtsolutions have in common? How do they differ? Whichsolutions have inflection points? At what population levelsdo they occur?(d) What are the equilibrium solutions? How are the othersolutions related to these solutions?where t is measured in weeks.(a) What is the carrying capacity? What is the value of k?(b) A direction field for this equation is shown. Whereare the slopes close to 0? Where are they largest?Which solutions are increasing? Which solutions aredecreasing?

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Step 1

Given that a population develops according to the logistic equation

Step 2

We know the Logistic Model equation is

Step 3

Now,

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