INTRAVENOUS INFUSION When a drug is administered with intravenous infusion, the amount of drug in patient's...
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INTRAVENOUS INFUSION When a drug is administered with intravenous infusion, the amount of drug in patient's blood- stream starts with zero and it increases until the rate the drug is entering the body equals the rate of drug is being eliminated from the body. The amount of drug in patient's bloodstream, A(t), t hours after an intravenous infusion begins can be modeled by A(t) = (1-¹) where r is the rate of infusion per hour and k is the exponential constant for the drug. [a.] Is A(t) an exponential decay function or an exponential growth function? Explain your reasoning Your Answer: This is an exponential decay that increases. This is because the quantity starts at zero when time is also zero. From there, there is an increase in the amount untill the rate reaches a certain point, from there the rate increase will slow as it approaches the rate the drugis being eliminated. [b.] Now, let's take a look the same drug that is used for the control of blood pressure in patients with severe hypertension. Suppose that this drug is given to the patient by intravenous infusion at a drip rate of 6mg/h. Recall that the half-life of this drug is 4 hours. Find a model for the amount of drug in patient's bloodstream t hours after the drug is administered (Round (r/-k) to a whole number), sketch the graph of A(t) using a computer, and find a horizontal asymptote for A(t). Your Answer: A(t)= 6mg/h (1-c*) at t = 1 A (t) = 6 at t = 4 A(t) = 12 INTRAVENOUS INFUSION When a drug is administered with intravenous infusion, the amount of drug in patient's blood- stream starts with zero and it increases until the rate the drug is entering the body equals the rate of drug is being eliminated from the body. The amount of drug in patient's bloodstream, A(t), t hours after an intravenous infusion begins can be modeled by A(t) = (1-¹) where r is the rate of infusion per hour and k is the exponential constant for the drug. [a.] Is A(t) an exponential decay function or an exponential growth function? Explain your reasoning Your Answer: This is an exponential decay that increases. This is because the quantity starts at zero when time is also zero. From there, there is an increase in the amount untill the rate reaches a certain point, from there the rate increase will slow as it approaches the rate the drugis being eliminated. [b.] Now, let's take a look the same drug that is used for the control of blood pressure in patients with severe hypertension. Suppose that this drug is given to the patient by intravenous infusion at a drip rate of 6mg/h. Recall that the half-life of this drug is 4 hours. Find a model for the amount of drug in patient's bloodstream t hours after the drug is administered (Round (r/-k) to a whole number), sketch the graph of A(t) using a computer, and find a horizontal asymptote for A(t). Your Answer: A(t)= 6mg/h (1-c*) at t = 1 A (t) = 6 at t = 4 A(t) = 12
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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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