Question

What are the solutions to the following diff eq’s?

A fish hatchery employed a mathematician to design a model to predict the population size of fish that the hatchery can expect to find in their pond at any given time. The mathematical model that the mathematician created is: dP dt 25 (a) Draw a one dimensional phase portrait of the autonomous differential equa- tion. What does this differential equation predict for future fish populations for various initial conditions? Describe the various cases in a few sentences interpreting your one-dimensional phase diagram (b) Solve the differential equation. Does your solution support your answer to part (a)? Why or why not? The hatchery was recently bought out by a corporation and the new owners are planning on allowing people to fish at the hatchery. So, the previous differential equation will no longer be a good prediction of the fish population at a given time. Below, find three possible differential equations that model the population of the fish in the hatchery, under the new assumption that people will be allowed to fish at the hatchery. Which of the three differential equations best models the new situation and why did you choose this one? (Assume the constant k represents the annual harvesting rate.) (a)2P 1 dt dt Based on the differential equation you chose from Question 2, prepare a one page report for the CEO of the corporation that explains the implications that various choices of the annua harvesting rate k wil have on future fish populations. You may include graphical representations in your report, but you must explain, in a concise way, the various effects the corporation's choice of the annual harvesting rate k w have on future fish populations

Answer 1

en tha 蛪.ap('.身 dt 1-D phase Poteait of this ealuahon is 95 as phese Poteait shows that fos an ial Populahon blo oto a15, the Populahon ω0ud rhoease, 2 fos an mita, populaton above as the Population ω0uld decbease Loith this twe Ccan Condlude he na Populion to be close to as Solving DE dt 35 45. P Plas-p) 95 P at -at cleanly at t=e0、Pa5 ashich is in suppos-l or obseavahon of Pat (a)