Suppose that the logistic equation dx/dt = kx(M x) models

Chapter 2, Problem 23P

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Problem 23P

Suppose that the logistic equation dx/dt = kx(M − x) models a population x(t) of fish in a lake after t months during which no fishing occurs. Now suppose that, because of fishing, fish are removed from the lake at the rate of lix fish per month (with h a positive constant). Thus fish are “harvested” at a rate proportional to the existing fish population, rather than at the constant rate of Example. (a) II 0 > h < kM, show that the population is Still logistic. What is the new limiting population? If

show that

so the lake is eventually fished out.

Questions & Answers

QUESTION:

Problem 23P

Suppose that the logistic equation dx/dt = kx(M − x) models a population x(t) of fish in a lake after t months during which no fishing occurs. Now suppose that, because of fishing, fish are removed from the lake at the rate of lix fish per month (with h a positive constant). Thus fish are “harvested” at a rate proportional to the existing fish population, rather than at the constant rate of Example. (a) II 0 > h < kM, show that the population is Still logistic. What is the new limiting population? If

show that

so the lake is eventually fished out.

ANSWER:

SOLUTION

Step 1 of 3

In this problem, we have to find the new limiting population and also we have to show that

if  


Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

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

Forgot password?
Register Now

×

Register

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