Question: I need help with these two problems please, and please make it legible. I have included the reference if it will help any. Section 4.4
I need help with these two problems please, and please make it legible. I have included the reference if it will help any.
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 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 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