Question: The simplest case of the logistic model is represented by the DE dy/dt = ky( I - y). Where k > 0 is the growth

The simplest case of the logistic model is represented by the DE
dy/dt = ky( I - y).
Where k > 0 is the growth rate constant Draw a direction field for this equation when k = I. Find the constant solutions. Explain why this model represents limited growth. What happens in the long run (that is, as t → ∞)?

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