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A certain drug is being administered intravenously to a hospital patient. of the drug enters the patient's bloodstream Fluid containing 4 mg cm³ 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 h. (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 mg h 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

A certain drug is being administered intravenously to a hospital patient. of the drug enters the patient's bloodstream Fluid containing 4 mg cm³ 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 h. (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 mg h 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

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A certain drug is being administered intravenously to a hospital patient. of the drug enters the patient's bloodstream Fluid containing 4 mg cm³ 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 h. (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 mg h 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
Transcribed Image Text:A certain drug is being administered intravenously to a hospital patient. of the drug enters the patient's bloodstream Fluid containing 4 mg cm³ 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 h. (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 mg h 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
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