Is it a good idea to harvest salmon at the maximal sustainable rate projected by this model?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
A company is considering starting to harvest salmon in a new region. They model the salmon population size in that region by the equation

\[ P'(t) = kP(t) - h, \]

with the natural growth rate of \( k = 2 \) salmon per year per population and a harvest rate \( h \) salmon per year. The company wants to decide how much salmon to harvest per year. The company estimates that currently there are 1 million salmon in that region.
Transcribed Image Text:A company is considering starting to harvest salmon in a new region. They model the salmon population size in that region by the equation \[ P'(t) = kP(t) - h, \] with the natural growth rate of \( k = 2 \) salmon per year per population and a harvest rate \( h \) salmon per year. The company wants to decide how much salmon to harvest per year. The company estimates that currently there are 1 million salmon in that region.
Is it a good idea to harvest salmon at the maximal sustainable rate projected by this model?
Transcribed Image Text:Is it a good idea to harvest salmon at the maximal sustainable rate projected by this model?
Expert Solution
Step 1: Given

Given that the equation P apostrophe left parenthesis t right parenthesis equals k P left parenthesis t right parenthesis minus h and k equals 2 comma P equals 1 comma t equals 0.

The objective is to state if it is a good idea to harvest at the maximum sustainable rate by this model.

steps

Step by step

Solved in 4 steps with 9 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
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,