Solved: (a) If a constant number h of fish are harvested from a fishery per unit time

Chapter 2, Problem 5

(choose chapter or problem)

(a) If a constant number h of fish are harvested from a fishery per unit time, then a model for the population P(t) of the fishery at time t is given by

\(\frac{d P}{d t}=P(a-b P)-h, \quad P(0)=P_{0}\),

where a, b, h, and \(P_{0}\) are positive constants. Suppose \(a=5\), \(b=1\), and \(h=4\).  Since the DE is autonomous, use the phase portrait concept of Section 2.1 to sketch representative solution curves corresponding to the cases \(P_{0}>4\), \(1<P_{0}<4\), and \(0<P_{0}<1\).  Determine the long-term behavior of the population in each case.

(b) Solve the IVP in part (a). Verify the results of your phase portrait in part (a) by using a graphing utility to plot the graph of P(t) with an initial condition taken from each of the three intervals given.

(c) Use the information in parts (a) and (b) to determine whether the fishery population becomes extinct in finite time. If so, find that time.

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer



Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now



Sign up for access to all content on our site!

Or login if you already have an account


Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back