Consider dxdt ax bx2 with a gt 0bgt 0 and x ge 0a how, Ask an Expert

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Consider dx/dt = ax + bx2 (with a > 0,b> 0, and x ≥ 0).

a) How does the growth rate depend on the population?

b) Sketch the one-dimensional phase line.

c) Sketch the time-dependent solution qualitatively.

d) From the exact solution, show that the population reaches infinity in a finite time; what might be called a population explosion.

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