If a drug is administered intravenously then the amount of drug in the bloodstream starts at...
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If a drug is administered intravenously then the amount of drug in the bloodstream starts at 0) and increases until the rate at which the drug enters the bloodstream (through the IV infusion) is equal to the rate at which it is leaving the bloodstream (through metabolization and elimination). It turns out that the amount of drug in the bloodstream hours after an IV infusion begins is B(t)=(1-ekt), where and are constants that depend on the drug and B(t) is measured in mg. If a drug is administered through rapid injection, instead of intravenously, then the amount of drug in the bloodstream starts out very high immediately after the injection, then decreases as the body. eliminates it. If a drug is administered by a rapid injection, followed by an IV infusion, then the amount of drug in the bloodstream after / hours is D(t) = Det + (1-ekt), where D is the initial injection dose. Suppose that for a certain drug k=-0.12. 18 1. Suppose that this drug will be administered through IV infusion with r= 6. Calculate lim B(t); what does your answer mean in terms of the model? Does that seem reasonable? Why or why not? 2. Again, suppose that this drug will be administered through IV infusion with = 6. Calculate the average rate of change of the amount of blood in the bloodstream during the first 24 hours of the IV infusion and during the second 24 hours. Which is larger? Does that seem reasonable? Why or why not? 3. Suppose now that we would like to ensure that the amount of drug in the bloodstream is exactly 60mg. Assuming that the initial dose is D = 60, use algebra to find the rate of infusion r that we should use. That is, find a number r for which D(t) = 60. If a drug is administered intravenously then the amount of drug in the bloodstream starts at 0) and increases until the rate at which the drug enters the bloodstream (through the IV infusion) is equal to the rate at which it is leaving the bloodstream (through metabolization and elimination). It turns out that the amount of drug in the bloodstream hours after an IV infusion begins is B(t)=(1-ekt), where and are constants that depend on the drug and B(t) is measured in mg. If a drug is administered through rapid injection, instead of intravenously, then the amount of drug in the bloodstream starts out very high immediately after the injection, then decreases as the body. eliminates it. If a drug is administered by a rapid injection, followed by an IV infusion, then the amount of drug in the bloodstream after / hours is D(t) = Det + (1-ekt), where D is the initial injection dose. Suppose that for a certain drug k=-0.12. 18 1. Suppose that this drug will be administered through IV infusion with r= 6. Calculate lim B(t); what does your answer mean in terms of the model? Does that seem reasonable? Why or why not? 2. Again, suppose that this drug will be administered through IV infusion with = 6. Calculate the average rate of change of the amount of blood in the bloodstream during the first 24 hours of the IV infusion and during the second 24 hours. Which is larger? Does that seem reasonable? Why or why not? 3. Suppose now that we would like to ensure that the amount of drug in the bloodstream is exactly 60mg. Assuming that the initial dose is D = 60, use algebra to find the rate of infusion r that we should use. That is, find a number r for which D(t) = 60.
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Related Book For
College Mathematics for Business Economics Life Sciences and Social Sciences
ISBN: 978-0321614001
12th edition
Authors: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Posted Date:
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