A biologist develops a culture that obeys the modified logistic equationwhere the “harvest...

A biologist develops a culture that obeys the modified logistic equation

where the “harvesting” is defined by the piecewise function

(a) Use a numerical solver to plot solution trajectories for initial bacterial populations ranging between 0 and 1000. You’ll note that in some cases, the population “recovers,” but in others, the bacterial count goes to zero. Determine experimentally the critical initial population that separates these two behaviors.

(b) Use an analytic method to determine the exact value of the “critical” initial population found in part (a). Justify your answer.