I'm needing help with these two problems, and I don't have any more information to give.

Example 4.2. The blue whale and fin whale are two similar species that inhabit the same areas. Hence, they are thought to compete. The intrinsic growth rate of each species is estimated at 5% per year for the blue whale and 8% per year for the fin whale. The environmental carrying capacity (the maximum number of whales that the environment can support) is estimated at 150,000 blues and 400,000 fins. The extent to which the whales compete is unknown. In the last 100 years intense harvesting has reduced the whale population to around 5,000 blues and 70,000 fins. Will the blue whale become extinct? Section 4.4 Exercise 6. Reconsider the whale problem of Example 4.2, and assume that a = 108. In this problem we will investigate the effects of harvesting on the two whale populations. Assume that a level of effort E boat days will result in the annual harvest of qEX1 blue whales and quz fin whales, where the parameter q (catchability) is assumed to be approximately 105. (a) Under what conditions can both species continue to coexist in the presence of harvesting? Use the five-step method, and model as a dynamical system in steady state. (b) Draw the vector field for this problem, assuming that the conditions identified in part (a) are satisfied. (c) Find the minimum level of effort required to reduce the fin whale population to its current level of around 70,000 whales. Assume that we started out with 150,000 blue whales and 400,000 fin whales before mankind began to harvest them. (d) Describe what would happen to the two populations if harvesting were allowed to continue at the level of effort identified in part (c). Draw the vector field in this case. This is the situation which lead the IWC to call for an international ban on whaling. Consider Guided Activity 2, Part 2, Task A: After finding the stable equilibrium point, we have that B = 57,000/1997*E + 276,000,000/1997. Using this and the fact Consider Guided Activity 2, Part 2, Task A: After finding the stable equilibrium p we have that F = -97,000/1997*E + 785,000,000/1997. Using this and the fact\fConsider Guided Activity 2, Part 2, Task C: Using the equation for F from Task A, and plugging in our F value in Task C, what is the value of E? Round your answer to the nearest whole number. Your Answer: Answer Consider Guided Activity 2, Part 2, Task D: Using the equation for B from Task A, and plugging in our E value from Task C, what is the value of B? Round your answer to the nearest whole number. Your Answer: Answer Section 4.4 Exercise 5. In the whale problem of Example 4.2 we used a logistic model of population growth, where the growth rate of population P in the absence of interspecies competition is p g(P) rP[1 E] In this problem we will be using a more complex model _ P-c _5 gm _rP[P +c][l K) in which the parameter c represents a minimum viable population level below which the growth rate is negative. Assume that the minimum viable population level is 3,000 for blue whales and 15,000 for fin whales. a) Can the two species of whales coexist? Use the five-step method, and model as a dynamical system in steady state. b) Sketch the vector field for this model. Classify each equilibrium point as stable or unstable. c) Assuming that there are currently 5,000 blue whales and 70,000 fin whales, what does this model predict about the future of the two populations. d) Suppose that we have underestimated the minimum viable population for the blue whale, and that it is actually closer to 10,000. Now what happens to the two species? r III I. L 'IIIHEFEIIHEIIL r I lll-llI-C' Complete Problem 6 from section 4.4 of your textbook. Your solution should be similar in scope to the example in this Module Two Guided Activity document, taking care to account for all steps in the fivestep model. You are welcome to first try solving the textbook problem on your own, but I am also going to include some steps and hints to help walk you through this portion as well in case you get stuck. Note: There are multiple ways to label these variables. 0 A classical mathematical way is to let x1 be the number of blue whales and x; be the number of fin whales. The textbook uses this. 0 For a specific application, it is often easier to name variables to be easier to remember. In our scripts, we use B for the number of blue whales and F for the number of fin whales