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Populations that can be modeled by the modified logistic equation dP = P(bP – a) | dt can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.005 and a = 0.4, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes. Initial population is 495 individuals b. Initial population is 53 individuals a. Population will trend towards extinction b. Doomsday scenario: Population will exhibit unbounded growth in finite time There is also a constant equilibrium solution for the population. Find this solution (note that the solution often is not a whole number, and hence unrealistic for population modeling). 80 P(t) : 1– 4e0.005 Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 495. 80 P(t) = 1- 0.84e0.005 Find the time T such that P(t) → 0 as t T. T = 34.87

Populations that can be modeled by the modified logistic equation dP = P(bP – a) | dt can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.005 and a = 0.4, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes. Initial population is 495 individuals b. Initial population is 53 individuals a. Population will trend towards extinction b. Doomsday scenario: Population will exhibit unbounded growth in finite time There is also a constant equilibrium solution for the population. Find this solution (note that the solution often is not a whole number, and hence unrealistic for population modeling). 80 P(t) : 1– 4e0.005 Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 495. 80 P(t) = 1- 0.84e0.005 Find the time T such that P(t) → 0 as t T. T = 34.87

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 2EA
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Populations that can be modeled by the modified logistic equation dP P(bP – a) dt can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.005 and a = behaviors will be exhibited by populations with the indicated initial sizes. 0.4, use phase portrait analysis to determine which of the two limiting %3D Initial population is 495 individuals b Initial population is 53 individuals a. Population will trend towards extinction b. Doomsday scenario: Population will exhibit unbounded growth in finite time There is also a constant equilibrium solution for the population. Find this solution (note that the solution often is not a whole number, and hence unrealistic for population modeling). 80 P(t) 1- 4e0.005 Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 495. 80 P(t) = 1- 0.84e0.005 Find the time T such that P(t) → ∞ ast T. T = 34.87
Transcribed Image Text:Populations that can be modeled by the modified logistic equation dP P(bP – a) dt can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.005 and a = behaviors will be exhibited by populations with the indicated initial sizes. 0.4, use phase portrait analysis to determine which of the two limiting %3D Initial population is 495 individuals b Initial population is 53 individuals a. Population will trend towards extinction b. Doomsday scenario: Population will exhibit unbounded growth in finite time There is also a constant equilibrium solution for the population. Find this solution (note that the solution often is not a whole number, and hence unrealistic for population modeling). 80 P(t) 1- 4e0.005 Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 495. 80 P(t) = 1- 0.84e0.005 Find the time T such that P(t) → ∞ ast T. T = 34.87
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