Question

# Show work . Ask the question.2. Select the modeling approach.3. Formulate the model.4. Solve the model.5....

Show work . Ask the question.2. Select the modeling approach.3. Formulate the model.4. Solve the model.5. Answer the question.Answer the following exercise:n 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:g(P) = rP(1 - P / K)andg(P) = rP (P - c / P + c) ( 1 - P / K )in which the parameter c represents a minimum viable population level below which the growth rate is negative. Assume that α =10-8 and that the minimum viable population level for is 3,000 for blue whales and 15,000 for fin whales.Our state variables for this equation are:B= Population of blue whalesF= Population of fin whalesState variables are the key variables for the system, which can often be thought of as the measurable variables. Here we are investigating population, so it makes sense that the state variables are the population of the two types of whales. There are some other variables that are important, but not necessarily state variables.gB= Growth rate of blue whale population (per year)gF= Growth rate of fin whale population (per year)cB= Competition factor for blue whale population (per year)cF= Competition factor for fin whale population (per year)Reconsider the whale problem of Example 4.2, and assume that α = 10​-8. 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 qEx2 ﬁn whales, where the parameter q (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 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 led the IWC to call for an international ban on whaling.