Populations that can be modeled by the modified logistic equation dP dt P(bP-a) can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.0015 and a = 0.18, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes. OT = a. Population will trend towards extinction b. Doomsday scenario: Population will exhibit unbounded growth in finite time a Initial population is 54 individuals b✓ Initial population is 283 individuals 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). P(t) = 120 Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 283. T= P(t) Find the time I such that P(t) → ∞ as t → T. =

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