The autonomous differential equations in Exercises 9–12 represent models for population growth. For each exercise, use a phase line analysis to sketch solution curves for P(t), selecting different starting values P(0). Which equilibria are stable, and which are unstable? 9.. dP/dt = 1 - 2P 10. dp/dt= 2P(P - 3) 11. dP/dt = P(1 - 2P) 12. dp/dt= 3P(1 - P)(P - 1 /2)
The autonomous differential equations in Exercises 9–12 represent models for population growth. For each exercise, use a phase line analysis to sketch solution curves for P(t), selecting different starting values P(0). Which equilibria are stable, and which are unstable?
9.. dP/dt = 1 - 2P
10. dp/dt= 2P(P - 3)
11. dP/dt = P(1 - 2P)
12. dp/dt= 3P(1 - P)(P - 1 /2)
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