Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Suppose that the equation dr = kr(M – x) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax %3D 2

Suppose that the equation dr = kr(M – x) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax %3D 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Suppose that the equation dr = kr(M – 1) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax 2 (d) If E 2 kM, show that r(t) → 0 as t → x, that is the lake is eventually fished out.
Transcribed Image Text:Suppose that the equation dr = kr(M – 1) – Er dt models the population of fish in a lake, where harvesting occurs at the rate of Ex fish per month (E a positive constant call harvesting effort). If 0 < E < kM, (a) If 0 < E < kM, show that the population is logistic. (b) What is the limiting population? kM (c) Show that the maximum sustainable harvesting effort is Emax 2 (d) If E 2 kM, show that r(t) → 0 as t → x, that is the lake is eventually fished out.
Expert Solution
steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS