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A certain drug is being administered intravenously to a hospital patien Fluid containing 4 mg cm³ of the drug enters the patient's bloodstream cm³ at a rate of 500 h The drug is absorbed by body tissues or otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.4 h¹¹. (a) Assuming that the drug is always uniformly distributed throughout the bloodstream, write a differential equation for the amount of drug that is present in the bloodstream at any time. Let M(t) be the total amount of the drug (in milligrams) in the patient's body at any given time t (in hours). NOTE: Use M as M (t). dM dt NOTE: Check your variables. Use a capital M (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. M mg h mg

A certain drug is being administered intravenously to a hospital patien Fluid containing 4 mg cm³ of the drug enters the patient's bloodstream cm³ at a rate of 500 h The drug is absorbed by body tissues or otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.4 h¹¹. (a) Assuming that the drug is always uniformly distributed throughout the bloodstream, write a differential equation for the amount of drug that is present in the bloodstream at any time. Let M(t) be the total amount of the drug (in milligrams) in the patient's body at any given time t (in hours). NOTE: Use M as M (t). dM dt NOTE: Check your variables. Use a capital M (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. M mg h mg

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A certain drug is being administered intravenously to a hospital patient Fluid containing 4 mg cm³ of the drug enters the patient's bloodstream cm³ at a rate of 500 h The drug is absorbed by body tissues or otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.4 h¹. (a) Assuming that the drug is always uniformly distributed throughout the bloodstream, write a differential equation for the amount of drug that is present in the bloodstream at any time. Let M(t) be the total amount of the drug (in milligrams) in the patient's body at any given time t (in hours). NOTE: Use M as M (t). dM dt NOTE: Check your variables. Use a capital M (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. M mg h mg
Transcribed Image Text:A certain drug is being administered intravenously to a hospital patient Fluid containing 4 mg cm³ of the drug enters the patient's bloodstream cm³ at a rate of 500 h The drug is absorbed by body tissues or otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.4 h¹. (a) Assuming that the drug is always uniformly distributed throughout the bloodstream, write a differential equation for the amount of drug that is present in the bloodstream at any time. Let M(t) be the total amount of the drug (in milligrams) in the patient's body at any given time t (in hours). NOTE: Use M as M (t). dM dt NOTE: Check your variables. Use a capital M (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. M mg h mg
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A certain drug is being administered intravenously to a hospital patient. of the drug enters the patient's bloodstream mg Fluid containing 4 cm³ at a rate of 500 -. The drug is absorbed by body tissues or h otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.4 h¹. cm³ 3 (a) Assuming that the drug is always uniformly distributed throughout the bloodstream, write a differential equation for the amount of drug that is present in the bloodstream at any time. Let M(t) be the total amount of the drug (in milligrams) in the patient's body at any given time t (in hours). NOTE: Use M as M (t). dM dt = 2000 0.4 M M = 50000 mg h (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. mg X
Transcribed Image Text:A certain drug is being administered intravenously to a hospital patient. of the drug enters the patient's bloodstream mg Fluid containing 4 cm³ at a rate of 500 -. The drug is absorbed by body tissues or h otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.4 h¹. cm³ 3 (a) Assuming that the drug is always uniformly distributed throughout the bloodstream, write a differential equation for the amount of drug that is present in the bloodstream at any time. Let M(t) be the total amount of the drug (in milligrams) in the patient's body at any given time t (in hours). NOTE: Use M as M (t). dM dt = 2000 0.4 M M = 50000 mg h (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. mg X
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