1. Applications of Exponential Functions of the Form y = ab* The half-life of a drug is an estimate of the period of time it takes for the concentration of the drug in the body to be reduced by exactly one half. Suppose the concentration C in mg/ml of a certain medication in terms of its half-life can be modeled by the function a. where A represents the initial dose of the medication in mg and t represents the number of hours since the initial dose. b. C. C(t) = A t 16 4 (1)³ If 20 mg of the medication was initially administered to a patient, what would be the concentration of the medication in 12 hours? Suppose the medication was administered 24 hours ago. If the concentration in the bloodstream is now 2 mg/ml, what was the initial dose? What does the function C(t) imply about the half-life of this particular medication? That is, how long will it take for the concentration of the drug to be cut in half?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Applications of Exponential Functions of the Form y
1.
The half-life of a drug is an estimate of the period of time it takes for the
concentration of the drug in the body to be reduced by exactly one half.
Suppose the concentration C in mg/ml of a certain medication in terms of its
half-life can be modeled by the function
a.
C.
= abx
where A represents the initial dose of the medication in mg and t represents the
number of hours since the initial dose.
b.
t
C (t) = A ( 1 ) ³
If 20 mg of the medication was initially administered to a patient, what
would be the concentration of the medication in 12 hours?
Suppose the medication was administered 24 hours ago. If the concentration
in the bloodstream is now 2 mg/ml, what was the initial dose?
What does the function C(t) imply about the half-life of this particular
medication? That is, how long will it take for the concentration of the drug to
be cut in half?
Transcribed Image Text:Applications of Exponential Functions of the Form y 1. The half-life of a drug is an estimate of the period of time it takes for the concentration of the drug in the body to be reduced by exactly one half. Suppose the concentration C in mg/ml of a certain medication in terms of its half-life can be modeled by the function a. C. = abx where A represents the initial dose of the medication in mg and t represents the number of hours since the initial dose. b. t C (t) = A ( 1 ) ³ If 20 mg of the medication was initially administered to a patient, what would be the concentration of the medication in 12 hours? Suppose the medication was administered 24 hours ago. If the concentration in the bloodstream is now 2 mg/ml, what was the initial dose? What does the function C(t) imply about the half-life of this particular medication? That is, how long will it take for the concentration of the drug to be cut in half?
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