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Suppose that when a patient takes a blood thinner drug at times t = 0, the amount of drug (in mg) in the patient's blood can be modelled by: A(t) = te¯kt where time t2 0 is measured in hours, and where k is some positive constant. (The domain of the function is D= [0, 00).) (a) Does the function A(t) have a horizontal asymptote (for t > 0)? Either compute the asymptote, or show that there is none. Would your answer change for different values of the positive constant k? (b) Write a sentence explaining what your answer in part (a) means for the patient. Does this seem reasonable? Explain briefly.

Suppose that when a patient takes a blood thinner drug at times t = 0, the amount of drug (in mg) in the patient's blood can be modelled by: A(t) = te¯kt where time t2 0 is measured in hours, and where k is some positive constant. (The domain of the function is D= [0, 00).) (a) Does the function A(t) have a horizontal asymptote (for t > 0)? Either compute the asymptote, or show that there is none. Would your answer change for different values of the positive constant k? (b) Write a sentence explaining what your answer in part (a) means for the patient. Does this seem reasonable? Explain briefly.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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1. Suppose that when a patient takes a blood thinner drug at times t = 0, the amount of drug (in mg) in the patient's blood can be modelled by: A(t) = te kt where time t2 0 is measured in hours, and where k is some positive constant. (The domain of the function is D (0, 00).) (a) Does the function A(t) have a horizontal asymptote (for t > 0)? Either compute the asymptote, or show that there is none. Would your answer change for different values of the positive constant k? (b) Write a sentence explaining what your answer in part (a) means for the patient. Does this seem reasonable? Explain briefly.
Transcribed Image Text:1. Suppose that when a patient takes a blood thinner drug at times t = 0, the amount of drug (in mg) in the patient's blood can be modelled by: A(t) = te kt where time t2 0 is measured in hours, and where k is some positive constant. (The domain of the function is D (0, 00).) (a) Does the function A(t) have a horizontal asymptote (for t > 0)? Either compute the asymptote, or show that there is none. Would your answer change for different values of the positive constant k? (b) Write a sentence explaining what your answer in part (a) means for the patient. Does this seem reasonable? Explain briefly.
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