5. Two drugs, Abraxane and Taxol, are both cancer treatments, yet have differing rates at which they leave a patient's system. Using terminology from pharmacology, Abraxane leaves the system by so-called "first-order elimination", which means that the concentration decreases at a constant percentage rate for each unit of time that passes. Taxol leaves the system by "zero-order elimina- tion", which means that the concentration decreases by a constant amount for each unit of time that passes. (a) As soon as the infusion of Taxol is completed, the drug concentration in a patient's blood is 1000 nanograms per milliliter (ng / ml). 12 hours later there is 50 ng / ml left in the patient's system. Use the data to construct an appropriate formula modeling the blood concentration of Taxol as a function of time after the infusion is completed.

5. Two drugs, Abraxane and Taxol, are both cancer treatments, yet have differing rates at which they leave a patient's system. Using terminology from pharmacology, Abraxane leaves the system by so-called "first-order elimination", which means that the concentration decreases at a constant percentage rate for each unit of time that passes. Taxol leaves the system by "zero-order elimina- tion", which means that the concentration decreases by a constant amount for each unit of time that passes. (a) As soon as the infusion of Taxol is completed, the drug concentration in a patient's blood is 1000 nanograms per milliliter (ng / ml). 12 hours later there is 50 ng / ml left in the patient's system. Use the data to construct an appropriate formula modeling the blood concentration of Taxol as a function of time after the infusion is completed.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(b) As soon as the infusion of Abraxane is completed, the drug concentration in a patient’s blood is 1000 nanograms per milliliter (ng/ml). 24 hours later there is 50 ng/ml left in the patient’s system. Use the data to construct an appropriate formula modeling the blood concentration of Abraxane as a function of time after the infusion is completed.

(c) Find the long-term behavior of the function from part (b). Is this behavior meaningful in the context of the model?

5. Two drugs, Abraxane and Taxol, are both cancer treatments, yet have differing rates at which they leave a patient’s system. Using terminology from pharmacology, Abraxane leaves the system by so-called “first-order elimination”, which means that the concentration decreases at a constant *percentage rate* for each unit of time that passes. Taxol leaves the system by “zero-order elimination”, which means that the concentration decreases by a constant *amount* for each unit of time that passes.

(a) As soon as the infusion of Taxol is completed, the drug concentration in a patient’s blood is 1000 nanograms per milliliter (ng/ml). 12 hours later there is 50 ng/ml left in the patient’s system. Use the data to construct an appropriate formula modeling the blood concentration of Taxol as a function of time after the infusion is completed.

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