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During surgery a patient receives midazolam, a sedative, to produce amnesia and ensure they do not remember the surgery. In a study, healthy volunteers take one injection of the drug at t = 0, and then measured the rate at which it disappeared from each volunteer's blood. If no further drug is added after t = 0, then the concentration will obey the differential equation: dC = -k,C dt Where k, is the fraction of drug eliminated per hour. a) Using the data below to find C(t). C(t) 64 36 1 3 b) During surgery midazolam may be infused continuous by intravenous line, at some constant rate a per milliliter of blood. Then the concentration must obey a differential equation. dC a – k,C dt Assuming that C(0) = 0 find C(t) as a function of t. c) Find lim C(t) in terms of a and k1.

During surgery a patient receives midazolam, a sedative, to produce amnesia and ensure they do not remember the surgery. In a study, healthy volunteers take one injection of the drug at t = 0, and then measured the rate at which it disappeared from each volunteer's blood. If no further drug is added after t = 0, then the concentration will obey the differential equation: dC = -k,C dt Where k, is the fraction of drug eliminated per hour. a) Using the data below to find C(t). C(t) 64 36 1 3 b) During surgery midazolam may be infused continuous by intravenous line, at some constant rate a per milliliter of blood. Then the concentration must obey a differential equation. dC a – k,C dt Assuming that C(0) = 0 find C(t) as a function of t. c) Find lim C(t) in terms of a and k1.

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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During surgery a patient receives midazolam, a sedative, to produce amnesia and ensure they do not remember the surgery. In a study, healthy volunteers take one injection of the drug at t = 0, and then measured the rate at which it disappeared from each volunteer's blood. If no further drug is added after t = 0, then the concentration will obey the differential equation: dC -k,C dt Where k, is the fraction of drug eliminated per hour. a) Using the data below to find C(t). C(t) 64 1 3 36 b) During surgery midazolam may be infused continuous by intravenous line, at some constant rate a per milliliter of blood. Then the concentration must obey a differential equation. dC = a - k,C dt Assuming that C(0) = 0 find C(t) as a function of t. %3D c) Find lim C(t) in terms of a and k1. 00-3
Transcribed Image Text:During surgery a patient receives midazolam, a sedative, to produce amnesia and ensure they do not remember the surgery. In a study, healthy volunteers take one injection of the drug at t = 0, and then measured the rate at which it disappeared from each volunteer's blood. If no further drug is added after t = 0, then the concentration will obey the differential equation: dC -k,C dt Where k, is the fraction of drug eliminated per hour. a) Using the data below to find C(t). C(t) 64 1 3 36 b) During surgery midazolam may be infused continuous by intravenous line, at some constant rate a per milliliter of blood. Then the concentration must obey a differential equation. dC = a - k,C dt Assuming that C(0) = 0 find C(t) as a function of t. %3D c) Find lim C(t) in terms of a and k1. 00-3
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