11. Consider the population modeldydt= 3y - y² - 2.This is a harvesting equation with a harvesting rate of 2. Find the steady states and theirstability, and interpret your answer in terms of the population model. Is this overhar-vesting, underharvesting, or critical harvesting?

11) Given:- The given population model is dydt=3y-y2-2. Here the harvesting rate is 2. To find:- The…

Answered: 11. Consider the population model dy dt…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. The DTDS given by P+1 = 3(P; + 18) describes a population in which 18 individuals are added to the population at the beginning of each generation and of that population survives. (a) Starting from a population of Po = 8 individuals, calculate the next three terms, that is, find P1, P2, and P3. (b) Calculate the equilibrium point of the model above. Show necessary algebra!
b) A metal component is subjected to heat-treatment called normalisation. The component is heated to a temperature T, (which is above the critical phase transformation temperatures) and cooled in air. The elementary change dT(t) of temperature T(t) of a heated component is determined from the heath energy balance equation cmdT(t) =-hA(T(t)– Tuir)dt where cmdT(t) is the energy which is lost due to cooling; hA(T(t)– Tuir )dt is the total heat flux from the component to the air during an infinitesimally small time interval dt. The constant c [J/(kg K)] is the specific heath capacity, m is the mass of the component in kg, h [W/(m? K)] is the heat transfer coefficient and A is the surface area in m?. Derive an equation which gives the temperature T(t) as a function of the cooling time t.
Please explain why this statement is true or false:"In the two-period model, both the Current Account and the Trade Balance in period one improve with an anticipated increase in the endowment of period two (ΔQ1=0 and ΔQ2>0)''Use equations of the optimal allocation of consumption in periods 1 and 2, the trade balance in period 1, and the current account in period 1 to support your answer.Assume the following lifetime utility function: U(C1,C2)= ln(C1) +β ln(C2) and the subjective discounting factor is 0<β<1
7. In the space provided below, discuss the AE (Keynesian cross), AD/AS, and ADI- IA models. What do they have in common? How do they differ? Which model do you prefer? Why? Pick one of the models and explain how you would use it to analyze the Bank of Canada’s recent hikes of the overnight rate target. Assume that the economy is experiencing an inflationary (expansionary) gap before the Bank of Canada decides to hike rates.
The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. 220- 210- 200- 190- 180- 170- 160- 150 140- 130 120- 110- 100- Year 0 3 90+ 801 6 9 12 15 Let S(t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is S(t) = 9.44t + 84.182. Retail Sales 85.851 108.426 141.781 169.256 202.297 222.266 3 6 9 12
Consider the discrete time model for population growth: Na+1 = Ne"(1-N,) with r > 0. (a) Find all steady states. (b) Discuss the stability of each steady state.
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What is the phase-line diagram of the function dP/dt = P3- 3P2 - 28P
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11. Consider the population model dy dt = 3y - y² - 2. This is a harvesting equation with a harvesting rate of 2. Find the steady states and their stability, and interpret your answer in terms of the population model. Is this overhar- vesting, underharvesting, or critical harvesting?