A population growing with harvesting will behaveaccording to the differential equationdyd.ty(0) = yo=C =0.02y (1у2800сFind the value for c for which there will be only oneequilibrium solution to the differential equationIf c is less than the value found above, there will beequilibria. If c isgreater than the value found above, there will beequilibria.

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Answered: A population growing with harvesting…

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. A patient is taking a medicine that has a half-life of 6 hours in the human body, meaning that the rate medicine is broken down is proportional to the amount present with constant of proportionality In 2 6 Starting at t = 0, they are on an IV drip that delivers a constant r mg per hour of medicine. Therefore, the differential equation satisfied by Q(t), the amount (in mg) of medicine in the patient's bloodstream at time t (in hours) is k = and the initial value problem is dQ dt =7- dQ dt Q(0) = 0. In 2 =7- Q₂ In 2 6 -Q₂ (a) Solve the initial value problem. (b) Suppose that the medicine requires 10 mg to be in the bloodstream to be effective. What values of r are appropriate if we want the patient to have at least 10 mg in their blood within three hours? (c) Unfortunately the medicine is toxic if there are ever 100 mg in the body. Keeping in mind we still want the patient to have effective levels after three hours, which values of r are also safe if the patient remains on the IV…
A person places Php 85,000 in a savings account which pays 13 percent interest per annum, compounded continuously. Find the time (in years) required for the account to double in value, presuming no withdrawals and no additional deposits.
The air in a crowded room full of people contains .25% carbon dioxide (CO2). An air conditioner is turned on that blows fresh air into the room at the rate of 500 cubic feet per minute. The fresh air mixes with the stale air, and the mixture leaves the room at the rate of 500 cubic feet per minute. The fresh air contains .01% CO2, and the room has a volume of 2500 cubic feet. (a) Find a differential equation satisfied by the amount f(t)of CO2 in the room at time t.(b) The model developed in part (a) ignores the CO2 produced by the respiration of the people in the room. Suppose that the people generate .08 cubic foot of CO2 per minute. Modify the differential equation in part (a) totake into account this additional source of CO2.
In 30 min
a continuing increase of the population on Earth eventually encourages settlement of the moon and mars. After colonization of the moon and mars, births rates continue to exceed death rates on earth, but life is hard away from earth so that the opposite is true elsewhere in the solar system. Nonetheles, the rising earth population constantly relocates the moon and Mars depending on the relative differences in population sizes. You have modelled the population dynamics via the following differential equations, where X1(t) is the Earth population at time t, X2(t) is the moon population, a and X3(t) is the population on mars. x`1 = -3/2 (x1-x2) - (x1-x3) + 3/2 x1 x`2 = -1/2 (x2 -x1) - 1/2(x2 -x3) - x2 x`3 = -1/2 (x3 -x1) - 1/2 (x3 -x2) - 1/2x1 a) if at time t=0 there are five bilion people on earth , and no one on moon and mars, Whats the population distribution far in the future? b) suppose instead that at a time t=0, 5/3 bilion people were on the moon, leaving 10/3 bilion on earth,…
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A tank originally contains 120 litre of brine with a salt concentration of 4 gram of salt per litre. Then brine with 15 gram of salt per litre is poured into the tank at a rate of 6 litre/minute, and the well-stirred mixture is allowed to leave at the same rate. a. Model this situation by a differential equation with initial conditions. b. Find the concentration of salt in the tank after 20 minutes. c. Find the eventual concentration of salt in the tank. (Hint: The eventual value will be as time goes to infinity.)
Disease epidemics can be modelled by differential equations. Suppose we have two sub-populations of individuals in a city: individuals who are infected with some virus (I) and individuals who are susceptible to infection (S). We assume that if a susceptible person interacts with an infected person, there is a probability p that the susceptible person will become infected. Each infected person recovers from the infection at a rate r and becomes susceptible again. The differential equations that model these population sizes are TI - PSI, dS dt dI dt pSI - TI. (a) Assuming no one dies from the virus, the total population N is a constant number defined as N = S+I. Show in this case that you can reduce the above system to the single differential equation for I. (b) Find the general solution I(t) to the ODE found in part (a). (c) If I (0) = Io, give the equation for the unknown constant in terms of Io, N, p and r.

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