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Suppose that a population model is the logistic model with harvesting term h, a constant, i.e.
dN/dt=N/ρ(1-kN)-h,
where ρ,k and h are positive constants such that ρk≤1/(4h).
(i) Find and classify the steady states N_1 and N_2, where N_1(ii) If the initial population is N_0 describe the future of the population for the three cases: (a) 0N_2.(iii) Show that there is a critical harvesting rate h_c so that if h>h_c then the population dies out regardless of the initial population. Express h_c in terms of ρ and k.(iv) Obtain the solution of the equation dN/dt=N/ρ(1-kN)-h with ρ=1 and k=1/10 for the harvesting rates h=1.6 and h=5.
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