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The drug Vicodin is eliminated from the bloodstream exponentially with a​ half-life of 36 hours. Suppose that a patient receives an initial dose of 40 milligrams of Vicodin at midnight.

a. How much Vicodin is in the​ patient's blood at noon on the first​ day?

b. Estimate when the Vicodin concentration will reach 50​% of its initial level.

a. How much Vicodin is in the​ patient's blood at noon on the first​ day?

There is approximately ______mg of Vicodin in the​ patient's blood at noon on the first day.

​(Round to the nearest tenth as​ needed.)

 Oct 1, 2020
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a -   12 midnight to 12 noon same day = 12 hours

V = 40 x 1/2^(12/36) =31.75 mg left in the bloodstream.

 

b - 20 = 40 x 1/2^(t/36), solve for t

t = 36 hours - as you might expect because it is the drug's "half-life"

 Oct 1, 2020

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