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Textbook 38.3 Consider Smith's model of population growth

`(dN)/(dt)=(\alpha N(f_(a)-\beta N))/(1+\alpha \gamma N),N(0)=N_(0).`

Here,

`\alpha ,f_(a),\beta ,\gamma ,N_(0)>0`

are constants. (a) Find the equilibrium populations. Hint: You do not need to explicitly solve (3). (b) Determine whether the equilibrium populations are stable or not. Hint: You do not need to explicitly solve (3). (c) Explicitly solve (3). Hint: Repeat, with modification, the process from question 2. (d) Calculate

`\lim_(t->\infty )N(t)`

.