26. Suppose the deer population P(1)in a small forest satisfies

the logistic equation

dP

dt

= 0.0225 P-0.0003 P².

Construct a slope field and appropriate solution curve to

answer the following questions: If there are 25 deer at

time = 0 and 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 hypothe-

ses of Theorem I are not satisfied, then the initial value prob-

lem y'= f(x, y), y(a) = b may have either no solutions,

finitely many solutions, or infinitely many solutions.