Populations that can be modeled by the modified logistic equation dP dt = P(6P-a) can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.002 and a = 0.16, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes. by Initial population is 9 individuals av Initial population is 237 individuals a. Doomsday scenario: Population will exhibit unbounded growth in finite time b. Population will trend towards extinction 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) Preview Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 237 P(t) Preview Find the time T such that P(t) + ast+T. T= 3 Preview Populations that can be modeled by the modified logistic equation dP dt = P(6P-a) can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b = 0.002 and a = 0.16, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes. by Initial population is 9 individuals av Initial population is 237 individuals a. Doomsday scenario: Population will exhibit unbounded growth in finite time b. Population will trend towards extinction 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) Preview Solve the modified logistic equation using the values of a and b given above, and an initial population of P(0) = 237 P(t) Preview Find the time T such that P(t) + ast+T. T= 3 Preview