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)
.

Question

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)

.

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