(Solved): Populations that can be modeled by the modified logistic equation dtdP=P(bPa) can either tren ...

Populations that can be modeled by the modified logistic equation $\frac{dP}{dt}=P(bP?a)$ can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If $b=0.003$ and $a=0.48$, 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 97 individuals Initial population is 597 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). $P(t)=$ Solve the modified logistic equation using the values of $a$ and $b$ given above, and an initial population of $P(0)=597$ $P(t)=?$ Find the time $T$ such that $P(t)??$ as $t?T$. $T=$