I need help with this problem please.

Example 4.2. The blue whale and n 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 n whale. The environmental carrying capacity (the maximum number of whales that the environment can support) is estimated at 150,000 blues and 400,000 ns. 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 ns. Will the blue whale become extinct? We will use the ve-step method. Notice that this problem is very similar to Example 4.1. Step 1 is to ask a question. We will use the number of blue and n whales as state variables and make the simplest possible assumptions about growth and competition. The question we begin with is this: Can the two populations of whales grow to stable equilibrium starting from their current levels? The results of step 1 are summarized in Figure 4.3. Variables: B = number of blue whales F = number of n whales 9;; = growth rate of blue whale population (per year) gp = growth rate of n whale population (per year) 05 = effect of competition on blue whales (whales per year) c1: = effect of competition on n whales (whales per year) Assumptions: 9;; = 0.058(1 3/150. 000) g;- = 0081\"\" - 19/400. 000) ca = c;- = 03!" B 2 0. F 2 0 a is a positive real constant Objective: Determine whether dynamic system can reach stable equilibrium starting from B = 5.000. F = 70.000 FIGURE 4.3 Results of step 1 for the whale problem. Step 2 is to select the modeling approach. We will model this problem as a dynamical system. A dynamical system consists of n state variables (x1,..., X,) and a system of differential equations (4.3) da1 = f1(21, . . . , In) dt dan = fn(21, . . ., Xin) dtThen the dynamical system equation is dd: (4.4) For a path x( t), the derivative dx/dt represents the velocity vector. Hence, for every solution curve x( t), we have that F(x(t)) is the velocity vector at each point. The vector eld F(x) tells us in what direction and how fast we are moving through the state space. Usually, a good idea of the qualitative behavior of a dynamical system in two variables can be obtained by drawing the vector eld at selected points. The points where F(x) = 0 are the equilibria, and we will pay special attention to the vector eld nearby these points. Step 3 is to formulate the model. Let x1 = B and x2 = F, and write 53,1: f1(x13 $2) 53% = f2(331, 502), where 51:1 (4.5) f1(:z:1, m2) 0.05131 1 m 1501132 f2(:z:1, $2) = 0.08332 1 m2 (2:31:32. _ 400,000 The state space is S ={(a:1,:1:2) :331 2 0,372 2 0}. 6. Reconsider the whale problem of Example 4.2, and assume that a = 10's. 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 qu1 blue whales and quz n whales, where the parameter 1] (catchability) is assumed to equal approximately 10'5. (a) Under what conditions can both species continue to coexist in the presence of harvesting? Use the ve-step method, and model as a dynamical system in steady state. (b) Draw the vector eld for this problem, assuming that the conditions identied in part (a) are satised. (c) Find the minimum level of effort required to reduce the n whale population to its current level of around 70,000 whales. Assume that we started out with 150,000 blue whales and 400,000 n 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 identied in part (c). Draw the vector eld in this case. This is the situation which led the IWC to call for an international ban on whaling. Consider Guided Activity 2, Part 2, Task B: Use the CoCalc output from this Task without harvesting (and including competition). Consider the equilibrium point that has non-zero values for both the B and F coordinates. What is the value of B at this equilibrium point? Round your answer to the nearest whole number. Your