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81. Pharmacology When a drug is administered orally, the amount of the drug present in the bloodstream of the patient can be modeled by a function of the form C(t) = ate-bt where C(t) is the concentration of the drug (in milligrams per liter), t is the number of hours since the drug was administered, and a and bare positive constants. For a 300 mg dose of the asthma drug aminophylline, this function is C (t) = 4.5te-0.275t (Source: Merck Manual of Diagnosis and Therapy) a. How much of this drug is present in the bloodstream at t = 0? b. How much of this drug is present in the bloodstream after 1 hour? c. Sketch the graph of this function, either by hand or with a graphing utility, with t ranging from 0 to 30. d. What happens to the value of the function as t→∞? Does this make sense in the context of this problem? Why? e. Use a graphing utility to find the time at which the concentration of this drug reaches its maximum. f. Use a graphing utility to determine when the concentration of this drug reaches 3 mg/L for the second time. (This will occur after the concentration peaks.)

81. Pharmacology When a drug is administered orally, the amount of the drug present in the bloodstream of the patient can be modeled by a function of the form C(t) = ate-bt where C(t) is the concentration of the drug (in milligrams per liter), t is the number of hours since the drug was administered, and a and bare positive constants. For a 300 mg dose of the asthma drug aminophylline, this function is C (t) = 4.5te-0.275t (Source: Merck Manual of Diagnosis and Therapy) a. How much of this drug is present in the bloodstream at t = 0? b. How much of this drug is present in the bloodstream after 1 hour? c. Sketch the graph of this function, either by hand or with a graphing utility, with t ranging from 0 to 30. d. What happens to the value of the function as t→∞? Does this make sense in the context of this problem? Why? e. Use a graphing utility to find the time at which the concentration of this drug reaches its maximum. f. Use a graphing utility to determine when the concentration of this drug reaches 3 mg/L for the second time. (This will occur after the concentration peaks.)

Advanced Engineering Mathematics
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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81. Pharmacology When a drug is administered orally, the amount of the drug present in the bloodstream of the patient can be modeled by a function of the form C(t) = ate-bt where C(t) is the concentration of the drug (in milligrams per liter), t is the number of hours since the drug was administered, and a and bare positive constants. For a 300 mg dose of the asthma drug aminophylline, this function is C (t) = 4.5te-0.275t (Source: Merck Manual of Diagnosis and Therapy) a. How much of this drug is present in the bloodstream at t = 0? b. How much of this drug is present in the bloodstream after 1 hour? c. Sketch the graph of this function, either by hand or with a graphing utility, with t ranging from 0 to 30. d. What happens to the value of the function as t→∞? Does this make sense in e context of this problem? Why? e. Use a graphing utility to find the time at which the concentration of this drug reaches its maximum. f. Use a graphing utility to determine when the concentration of this drug reaches 3 mg/L for the second time. (This will occur after the concentration peaks.)
Transcribed Image Text:81. Pharmacology When a drug is administered orally, the amount of the drug present in the bloodstream of the patient can be modeled by a function of the form C(t) = ate-bt where C(t) is the concentration of the drug (in milligrams per liter), t is the number of hours since the drug was administered, and a and bare positive constants. For a 300 mg dose of the asthma drug aminophylline, this function is C (t) = 4.5te-0.275t (Source: Merck Manual of Diagnosis and Therapy) a. How much of this drug is present in the bloodstream at t = 0? b. How much of this drug is present in the bloodstream after 1 hour? c. Sketch the graph of this function, either by hand or with a graphing utility, with t ranging from 0 to 30. d. What happens to the value of the function as t→∞? Does this make sense in e context of this problem? Why? e. Use a graphing utility to find the time at which the concentration of this drug reaches its maximum. f. Use a graphing utility to determine when the concentration of this drug reaches 3 mg/L for the second time. (This will occur after the concentration peaks.)
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