Example: • A drug is administered to a patient through an intravenous line at a rate of 6 mg/hr. • The drug's presence in the body (drug load) is reduced, through metabolic and other chemical processes, at a rate of 3% per hour. = -0.03y + 6 dt In this example, -0.03y represents 3% of the current drug load in the body, and is the change in drug load in the body, in units of mg per hour. The function y (t) is not known, but it represents the patient's drug load at time t (in hours). Notice, the quantity of drug metabolized out of the system depends on the current drug load (-0.03y) but the quantity of drug added to the patient through the intravenous therapy is constant eac hour (+6). You try one: • The amount of drug in the blood of a patient (in mg) due to an intravenous line is described by = -0.02y + 3, where t is measured in hours. In this problem, reduction of 2% OR addition through intravenous line of 2% • -0.02y represents [Select ] of the drug load; addition of doses each hour through the intravenous line OR • +3 represents ( Select ] addition of 3% each hour due to metabolic processes • and is the rate of change, in units of ( Select ] mg/hr OR mg/year OR percent/hour
Example: • A drug is administered to a patient through an intravenous line at a rate of 6 mg/hr. • The drug's presence in the body (drug load) is reduced, through metabolic and other chemical processes, at a rate of 3% per hour. = -0.03y + 6 dt In this example, -0.03y represents 3% of the current drug load in the body, and is the change in drug load in the body, in units of mg per hour. The function y (t) is not known, but it represents the patient's drug load at time t (in hours). Notice, the quantity of drug metabolized out of the system depends on the current drug load (-0.03y) but the quantity of drug added to the patient through the intravenous therapy is constant eac hour (+6). You try one: • The amount of drug in the blood of a patient (in mg) due to an intravenous line is described by = -0.02y + 3, where t is measured in hours. In this problem, reduction of 2% OR addition through intravenous line of 2% • -0.02y represents [Select ] of the drug load; addition of doses each hour through the intravenous line OR • +3 represents ( Select ] addition of 3% each hour due to metabolic processes • and is the rate of change, in units of ( Select ] mg/hr OR mg/year OR percent/hour
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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![Example:
• A drug is administered to a patient through an intravenous line at a rate of 6 mg/hr.
• The drug's presence in the body (drug load) is reduced, through metabolic and other chemical processes, at a rate of 3% per hour.
dy
:-0.03y + 6
dt
dy
In this example, –0.03y represents 3% of the current drug load in the body, and is the change in drug load in the body, in units of mg per hour.
The function y (t) is not known, but it represents the patient's drug load at time t (in hours).
Notice, the quantity of drug metabolized out of the system depends on the current drug load (–0.03y) but the quantity of drug added to the patient through the intravenous therapy is constant each
hour (+6).
You try one:
• The amount of drug in the blood of a patient (in mg) due to an intravenous line is described by “ = -0.02y + 3, where t is measured in hours.
dt
In this problem,
reduction of 2% OR addition through intravenous line of 2%
• -0.02y represents
[ Select ]
of the drug load;
OR
addition of doses each hour through the intravenous line
+3 represents [Select]
addition of 3% each hour due to metabolic processes
dy
• and
is the rate of change, in units of [Select ],
dt
mg/hr OR mg/year OR percent/hour](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3b1948a-718d-4620-a4c2-56e99440ab60%2Fbef869d8-1153-40a4-a1ec-c9b5ff47d7b3%2F8qurme9_processed.png&w=3840&q=75)
Transcribed Image Text:Example:
• A drug is administered to a patient through an intravenous line at a rate of 6 mg/hr.
• The drug's presence in the body (drug load) is reduced, through metabolic and other chemical processes, at a rate of 3% per hour.
dy
:-0.03y + 6
dt
dy
In this example, –0.03y represents 3% of the current drug load in the body, and is the change in drug load in the body, in units of mg per hour.
The function y (t) is not known, but it represents the patient's drug load at time t (in hours).
Notice, the quantity of drug metabolized out of the system depends on the current drug load (–0.03y) but the quantity of drug added to the patient through the intravenous therapy is constant each
hour (+6).
You try one:
• The amount of drug in the blood of a patient (in mg) due to an intravenous line is described by “ = -0.02y + 3, where t is measured in hours.
dt
In this problem,
reduction of 2% OR addition through intravenous line of 2%
• -0.02y represents
[ Select ]
of the drug load;
OR
addition of doses each hour through the intravenous line
+3 represents [Select]
addition of 3% each hour due to metabolic processes
dy
• and
is the rate of change, in units of [Select ],
dt
mg/hr OR mg/year OR percent/hour
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