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categoryرياضيات
schoolبكالوريوس
event_available2026-07-13
السؤال
Transcribed Image Text:
10.
For a fish population modeled by a depensation growth model, we have,
when there is harvesting,
dt
N= F(N)-H(N).
where
and H(N)=qEN.
F(N) N (N/N-1)(1 - N/K)
a. Find (and plot, freehand) the sustained yield H(N) as a function
of effort E, and the unsustainable yield H(N2), also as a function
of E (and plot on the same figure). Here N is the nontrivial stable
equilibrium of N and N is the unstable equilibrium.
b. Find the E(= Emax), where the two curves in (a) merge (this happens
when N = N3). What happens to the fishery and the fish population
when E Emax?
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c. Suppose harvesting is done at effort level E = Emax for a while so that
the fish population is below what was thought of as the "sustainable"
N (which is equal to N₂, so actually it is not really sustainable).
Realizing that there is a problem, the government puts in a fishing
limit that reduces the effort E to slightly below Emax. Can the fishery
recover?
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