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10 Nov 2019
Any population, P, for which we can ignore immigration, satisfies Dp/dt= Birth rate - Death rate. For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population Thus, the population of such a type of organism satisfies a differential equation of the form This problem investigates the solutions to such an equation. (a) Sketch a graph of dP/dt against P. Note when dP/dt is positive and negative. dP/dt 0 when P is in (b) Use this graph to sketch the shape of solution curves with various initial values: use your answers in part (a), and where dP/dt is increasing and decreasing to decide what the shape of the curves has to be Based on your solution curves, why is P = b/a called the threshold population? If P(0) > b/a, what happens to P in the long run? If P(0) = b/a, what happens to P in the long run? If P(0)
Any population, P, for which we can ignore immigration, satisfies Dp/dt= Birth rate - Death rate. For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population Thus, the population of such a type of organism satisfies a differential equation of the form This problem investigates the solutions to such an equation. (a) Sketch a graph of dP/dt against P. Note when dP/dt is positive and negative. dP/dt 0 when P is in (b) Use this graph to sketch the shape of solution curves with various initial values: use your answers in part (a), and where dP/dt is increasing and decreasing to decide what the shape of the curves has to be Based on your solution curves, why is P = b/a called the threshold population? If P(0) > b/a, what happens to P in the long run? If P(0) = b/a, what happens to P in the long run? If P(0)
Patrina SchowalterLv2
11 Jun 2019