Gce Model Questions Vol1 2023 Agricultural Science Question 49

Practice objective / multiple choice question 49 from the 2023 Gce Model Questions Vol1 Agricultural Science examination.

Gce Model Questions Vol1 2023 Agricultural Science Objective / Multiple Choice Hard Difficulty
Question 49 GCE_MODEL_QUESTIONS_VOL1 • 2023 • AGRICULTURAL_SCIENCE • objective

A fish population in a lake follows logistic growth described by \(\frac{dN}{dt}=rN\left(1-\frac{N}{K}\right)\), where \(r=0.5\ \text{yr}^{-1}\) and \(K=200\,000\) fish. (a) If a constant annual harvest \(H\) is taken, the population will be at equilibrium when \(\frac{dN}{dt}=0\). Determine the maximum sustainable harvest \(H_{\max}\) and the corresponding equilibrium population size. (b) If instead the fishery harvests 30 % of the equilibrium population each year, calculate the new equilibrium population size and the annual harvest.

Answer Options

A. H_max = 25,000 fish yr⁻¹ at N = 120,000 fish; with a 30 % harvest the new equilibrium is N = 84,000 fish (harvest = 25,200 fish yr⁻¹)
Correct Answer B. H_max = 25,000 fish yr⁻¹ at N = 100,000 fish; with a 30 % harvest the new equilibrium is N = 80,000 fish (harvest = 24,000 fish yr⁻¹)
C. H_max = 20,000 fish yr⁻¹ at N = 100,000 fish; with a 30 % harvest the new equilibrium is N = 85,000 fish (harvest = 25,500 fish yr⁻¹)
D. H_max = 30,000 fish yr⁻¹ at N = 100,000 fish; with a 30 % harvest the new equilibrium is N = 70,000 fish (harvest = 21,000 fish yr⁻¹)
Correct Answer
B
Correct Option:
H_max = 25,000 fish yr⁻¹ at N = 100,000 fish; with a 30 % harvest the new equilibrium is N = 80,000 fish (harvest = 24,000 fish yr⁻¹)

About This Question

This is Gce Model Questions Vol1 2023 Agricultural Science Question 49. It is one of the objective questions from the 2023 Gce Model Questions Vol1 Agricultural Science examination.

Difficulty level: Hard .

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