Consider a population r(t) of fish in a lake governed by the logistic equation r' = x(4-2), where a is in hundreds of fish and t is in years. See the slope field of the equation below. 111010, 18) 1 " A(0,6)' (a) () Draw a phase diagram and label all critical points as stable or unstable. (b) (c) (d) B/0 1.5 Now consider the same population, where we account for fishing in the lake that reduces the population by 300 fish per year. This is now a logistic population with harvesting. given by the equation r' = x(4-x) - 3. See its slope field below. Solve this equation with the same initial condition z(0) = 1.5. c(0, 0.5) 1 Solve the logistic equation, given that the initial population is 150 fish. 1 What will be the limiting population in the lake after many years? " A(0, 11 NA ( What will the new limiting number of fish in the lake be, now that we are taking fishing into account? Logistic populations with harvesting have a threshold population. If the initial popu- lation is below this threshold, the population will decrease, leading to extinction. What is the threshold population of this equation?