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A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 5 cm3 of the drug enters the patient's bloodstream 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 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 dt h 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.

A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 5 cm3 of the drug enters the patient's bloodstream 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 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 dt h 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.

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. Fluid containing 5 mg of the drug enters the patient's bloodstream cm3 cm3 The drug is absorbed by body tissues or h at a rate of 500 otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.4 hl. (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 dt h 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. Fluid containing 5 mg of the drug enters the patient's bloodstream cm3 cm3 The drug is absorbed by body tissues or h at a rate of 500 otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.4 hl. (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 dt h 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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