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.