5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetizedwhen its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol perkilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminatedfrom the dog's bloodstream at a rate which is proportional to the amount of sodiumpentobarbitol in the bloodstream and that after 5 hours half of the initially prescribedsodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial valuedifferential equation. What single dose should be administered in order to anesthetize a 50-kgdog for 1 hr?

Answered: Image /qna-images/answer/f17334bf-8396-425c-8b25-043189ec45ec.jpg

Answered: 5. Suppose that sodium pentobarbital is…

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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1. At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing into the tank at a rate of 2 L per hour and the well-mixed solution flows out of the tank at a rate of 3 L per hour. At What time will the tank contain 100 g of salt (or will the tank empty before this happens)? 2. At 12:00 p.m. the next day, another tank contains 150 g of salt dissolved in 8 L of water. Water containing 10 g of salt per L begins flowing into the tank at a rate of 2 L per hour and the well-mixed solution flows out of the tank at the same rate. At What time will the tank contain 100 g of salt (or will this never happen)?
(b). Consider 2 intercomected tank. Tank A initially contains 18⁰ L of water and log of salt, and tank B Initially contains looL of water and 25g of salt. The Liquid inside each tank is kept well stirred. Liquid flows from tank A to tank B at a rate of BL/min and liquid flows from tank B to tank A at rate of 34lmin. A salt brine with connectration 179/L of salt flows into tank A at a rate of 4 L/min and the solution drains out at 4 L/min. i). Draw a collection of tanks diagram such that all flow rates, volumes, and the incoming salt concentration are shown on it. ii). Write out a system of first-order linear differential equations that would describle the rates of charge of the concentrations of salt, Cilt), (zlt). Do not forget to write the initial conditions. Do not save the equations.
The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 40 minutes it is observed that 100 bacteria are present. After 1 hour 80 bacteria are present. What was the initial number of bacteria?
(2) 8. Two gears, one with 15 teeth and the other one with 20 teeth, fit together as shown in this diagram. When the smaller gear has rotated 20 times, how many times has the larger gear rotated? A tank with a capacity of 5 000 e is being filled by a pipe that delivers water at a rate of 200 ml/s. 9. How long will it take to fill the tank? Give your answer in hours, minutes and seconds. a) If water leaks out of the tank at a rate of 3 ml/s as it is being filled, how long will it now b) take to fill the tank? Give your answer in hours, minutes and seconds. (2) (2)
The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours it is observed that 500 bacteria are present. After 10 hours 5000 bacteria are present. What was the initial number of bacteria?
Find foo fo x² (x²+4) (x²+2x+2) x² +24+2) d dx
20. A 13 foot ladder leans against a vertical wall. When the ladder is pulled away from the wall at a rate of 0.5 ft/s, how fast is the top of the ladder sliding down the wall when the foot of the ladder is 5 ft away from the wall? 13 ft
A certain radioactive material is known to decay at a rate proportional to the amount present. Initially there is 50 mg of the material present and after 2 hours it is observed that the material has lost 10 percent of its original mass, Determine the mass of the material after 4 hours.
5. A normal saline solution (0.9 mg of sodium chloride per 100 ml of solution) is given intravenously and a total of 0.5 L of the solution was given over a 4 hour period. (e) What is the flow rate in units of milliliter per hour?. (b) What is the flow rate in units of mg (of sodium chloride) per hour. (c) During 4 hour period how much sodium chloride is delivered?.
A tank contains 1000L of pure water. Brine that contains 0.02kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.07kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions. 1. How much salt is in the tank after t minutes? Answer (in kilograms): S(t) = ... 2. How much salt is in the tank after 5 hours? Answer (in kilograms):
4. A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.2 kg/L, deter- mine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.1 kg/L?
9. A patient weighing 70 kg should receive a dose of 1400 units of rabies immune globulin after exposure to rabies. How much of a solution containing 900 units per 3 mL should be injected for this dose? 10. Zoster Vaccine Live (ZOSTAVAX) contains 19,400 plaque-forming units (PFU) of attenuated virus per 0.65 mL. What is the concentration expressed as PFU/mL?

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