Gce Model Questions Vol1 2022 Biology Question 48

Practice objective / multiple choice question 48 from the 2022 Gce Model Questions Vol1 Biology examination.

Gce Model Questions Vol1 2022 Biology Objective / Multiple Choice Hard Difficulty
Question 48 GCE_MODEL_QUESTIONS_VOL1 • 2022 • BIOLOGY • objective

A fish population in a lake follows logistic growth with intrinsic rate \(r = 0.4\ \text{yr}^{-1}\) and carrying capacity \(K = 200{,}000\) individuals. Two harvesting strategies are proposed: A. A constant annual harvest of \(H\) fish; B. An annual harvest equal to \(10\%\) of the current population size. (a) Determine the maximum constant harvest \(H_{\max}\) that can be sustained indefinitely without driving the population to extinction. (b) If the constant harvest is set at \(80\%\) of \(H_{\max}\), calculate the equilibrium population size under strategy A. (c) Using the same initial population (\(N_{0}=K\)) and a 10‑year horizon, compute the total number of fish harvested under strategy B and the average annual yield. Compare this average yield with the constant harvest of part (b) and state which strategy provides the higher sustainable yield.

Answer Options

A. H_max = 22,500 fish\/yr; equilibrium under 80% H_max ≈ 150,000 fish; total harvested under strategy B ≈ 152,500 fish (average ≈ 15,250 fish\/yr); strategy B gives the higher yield (15,250 fish\/yr).
B. H_max = 18,000 fish\/yr; equilibrium under 80% H_max ≈ 138,000 fish; total harvested under strategy B ≈ 140,000 fish (average ≈ 14,000 fish\/yr); strategy A gives the higher yield (14,400 fish\/yr).
C. H_max = 20,000 fish\/yr; equilibrium under 80% H_max ≈ 130,000 fish; total harvested under strategy B ≈ 135,000 fish (average ≈ 13,500 fish\/yr); strategy A gives the higher yield (16,000 fish\/yr).
Correct Answer D. H_max = 20,000 fish/yr; equilibrium under 80% H_max ≈ 144,722 fish; total harvested under strategy B ≈ 147,369 fish (average ≈ 14,737 fish/yr); strategy A gives the higher yield (16,000 fish/yr).
Correct Answer
D
Correct Option:
H_max = 20,000 fish/yr; equilibrium under 80% H_max ≈ 144,722 fish; total harvested under strategy B ≈ 147,369 fish (average ≈ 14,737 fish/yr); strategy A gives the higher yield (16,000 fish/yr).

About This Question

This is Gce Model Questions Vol1 2022 Biology Question 48. It is one of the objective questions from the 2022 Gce Model Questions Vol1 Biology examination.

Difficulty level: Hard .

View More Gce Model Questions Vol1 2022 Biology Questions More Gce Model Questions Vol1 Practice Questions Back to Questions

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Chat with Support