Suppose the deer population P(l) in a small forest satisfies the logistic equationConstruc...

Suppose the deer population P(l) in a small forest satisfies the logistic equation

Construct a slope field and appropriate solution curve to answer the following questions: If there are 25 deer at time t = 0 and t is measured in months, how long will it take the number of deer to double? What will be the limiting deer population?

The next seven problems illustrate the fact that, if the hypotheses of Theorem 1 are not satisfied, then the initial value problem y′ = f(x, y), y(a) = b may have either no solutions, finitely many solutions, or infinitely many solutions.