Question 2 A patient takes d mg of medicine every 8 hours. Every 8 hours, 80% of the medicine in the patient'sbloodstream is eliminated. The medicine has side effects if there is ever 15 mg or more in the patient'sblood, but there needs to be at least 2 mg in the patient's blood for it to be effective.(a) What is the maximum safe value for d? (Hint: Consider An, the amount of medicine in thepatient's blood immediately after taking the nth dose, and think about what must be true aboutAn to ensure a safe dosing schedule. Write out very carefully what A1, A2, Az are before tryingto find a pattern for An.)(b) What is the minimum effective value for d? (Hint: Consider Bn, the amount of medicine in thepatient's blood immediately before taking the nth dose.)

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Answered: 2 A patient takes d mg of medicine…

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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The Krill which are tiny shrimplike creatures are the principal food source for the huge blue whale. The intrinsic growth rate and the carrying capacity of the blue whale are estimated at 5% per year and 150,000 respectively. The maximum sustainable population for krill is 600 tons/acre. In the absence of predators, in uncrowded conditions, the krill population grows at a rate of 20% per year. The pres-ence of 600 tons/acre of krill increases blue whale population growth rate by 2.5% per year, and the presence of 150,000 blue whales decreases krill growth rate by 8% per year. (a) Determine all the steady states of the system and analyze theri stability. Can the blue whales and the krill coexist? (b) Verify your conclusion of stability by plotting the solution and the vector fields for selected values of initial populations. (c) Describe what happens to the two populations over time. Assume that we start o with 10,000 blue whales and 500 tons/acre of krill. (d) How sensitive are…
A tank contains 500 gallons of water with 100 gallons of pollution dissolved in it. Polluted water containing 2 lb of sludge per gallon enters the tank at a rate of 4 gallons/hour. The solution is thoroughly mixed and drains from the tank at a rate of 5 gallon/hour. Find a formula for the concentration of pollutants at time t. Sketch the graph of the concentration over time (you are welcome to use a graphing calculator), clearly showing the valid domain for your solution.
3. The half-life of caffeine is 5 hours. If you drink coffee with 200mg of caffeine, how much caffeine will be in your system in 12 hours? Show work to support your answer.
Suppose: • The vat contains 270 gallons of liquid, which • • . never changes. Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 30 gallons/minute. Sugar water with a concentration of 8 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. • The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 65 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 32 tablespoons of sugar in the vat at t = present 4 minutes later? 0. How many tablespoons will be tablespoons
13 A patient with peptic ulcer disease has an order for famotidine 20 mg IVPB q 12 h over 15 minutes. The famotidine is diluted in 25 mL of D5W. The tubing drop factor is 20 gtt/mL. How many drops per minute should be given?
(i) Using the integral definition below, find the average density of the Earth given the following information: Oceanic Plate where can be written as 3-5 miles thick ● Diagram not drawn to scale 1400 miles Thick 1800 miles thick 5-25 miles thick 800 miles thick Continental Plate Mantle (Flows with the consistancy of asphalt) Scale everything in terms of the radius of the Earth R ( 4000 miles here for simplicity), so that in terms of the variable y r/R, 0 ≤ y ≤ 1, the integral for the average density p=2³3r²p(r)dr Outer Core (Iron and nickel in the liquid state) Inner Core (Iron and nickel in the solid state} p=3√ 1²p(v)dy, p(y) = P₁, 0≤ y ≤yi, = P2, y1 ≤y ≤y2, = P3, y2 ≤y ≤ y3, = P4, Y3 ≤ y ≤ 1. INNER CORE (0 ≤ y ≤ yı): Earth's inner core has the highest density p₁ 13 g/cm³. OUTER CORE (1 ≤ y ≤ y2): Next, the outer core has a density P2 11 g/cm³. LOWER MANTLE (y2 ≤ y ≤y3): The lower mantle has a significantly lower density P35 g/cm³. This is about 1400 miles thick.
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Sodium Pentathol Elimination Ed is undergoing surgery for an old football injury and must be anesthetized. The anesthesiologist knows Ed will be "under" when the concentration of sodium pentathol in his blood is at least 50 milligrams per kilogram of body weight. Suppose that Ed weighs 1 00 kg (220 pounds) and that sodium pentathol is eliminated from the bloodstream al a ra1e proponional 10 lhe amount present. If the half-life of 1he drug is 10 hours, whal single dose should be given to keep Ed anesthetized for three hours?
the sales revenue of a new mobile phone model is found to follow an AR(1) process, as shown below. what is the 3-lag AČF value? Xt =0.7*xt-1+Wt 0.700 .0.343 0.490 0.240
A large tank is filled to capacity with 700 gallons of pure water. Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 7 gal/min. The well-mixed solution is pumped out at a rate of 14 gals/min. Find the number A(t) of pounds of salt in the tank at time t. A(t) =. lb
Can you find the amount of salt A in the tank at any time t?

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