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11 Nov 2019
Assume that two colonies each have 1500 members at time t = 0 and that each evolves with a constant relative birth rate k = rb - rd. For colony 1, assume that individuals migrate into the colony at a rate of 30 individuals per unit time. Assume that this immigration occurs for 0 t 1 and ceases thereafter. For colony 2, assume that a similar migration pattern occurs but is delayed by one unit of time; that is, individuals immigrate at a rate of 30 individuals per unit time. 1 t 2. Suppose we are interested in comparing the evolution of these two populations over the time interval 0 t 2. The initial value problems governing the two populations are Solve both problems to find P1 and P2 at time t = 2. P1(2) = P2(2) = Show that P1(2) - P2(2) = 30/k (ek - 1)2. If k > 0, which population is larger at time t = 2? If k
Assume that two colonies each have 1500 members at time t = 0 and that each evolves with a constant relative birth rate k = rb - rd. For colony 1, assume that individuals migrate into the colony at a rate of 30 individuals per unit time. Assume that this immigration occurs for 0 t 1 and ceases thereafter. For colony 2, assume that a similar migration pattern occurs but is delayed by one unit of time; that is, individuals immigrate at a rate of 30 individuals per unit time. 1 t 2. Suppose we are interested in comparing the evolution of these two populations over the time interval 0 t 2. The initial value problems governing the two populations are Solve both problems to find P1 and P2 at time t = 2. P1(2) = P2(2) = Show that P1(2) - P2(2) = 30/k (ek - 1)2. If k > 0, which population is larger at time t = 2? If k