Math  /  Calculus

QuestionIf tt is in minutes since the drug was administered, the concentration, C(t)inng/mlC(t) \mathrm{in} \mathrm{ng} / \mathrm{ml}, of a drug in a patient's bloodstream is given by C(t)=20te0.04tC(t)=20 t e^{-0.04 t}. (a) How long does it take for the drug to reach peak concentration? What is the peak concentration?
Round your answers to one decimal place.
The drug reaches its peak concentration at i \square minutes.
The peak concentration is i \square ng/ml\mathrm{ng} / \mathrm{ml}. (b) What is the concentration of the drug in the body after 15 minutes? After an hour?
Round your answers to one decimal place. The concentration after 15 minutes is \square ng/ml\mathrm{ng} / \mathrm{ml}.
The concentration after 60 minutes is \square i ng/ml\mathrm{ng} / \mathrm{ml}. (c) If the minimum effective concentration is 10ng/ml10 \mathrm{ng} / \mathrm{ml}, when should the next dose be administered? cytosolic proteins cytoso

Studdy Solution
(a) The drug reaches its peak concentration at 25.0\textbf{25.0} minutes.
The peak concentration is 183.9\textbf{183.9} ng/ml. (b) The concentration after 15 minutes is 164.6\textbf{164.6} ng/ml.
The concentration after 60 minutes is 108.8\textbf{108.8} ng/ml. (c) The next dose should be administered after approximately 113.2\textbf{113.2} minutes.

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