Question
Asked Oct 14, 2019
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A patient is adminstered a dose of

70mg of a drug. If the body naturally disposes of 5% of the drug every​ hour, how quickly will the amount of the drug be changing​ (in mg/hr) 5 hours after​ ingestion?
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Expert Answer

Step 1

Given,

           A patient is administered a dose of 70mg of a drug and the body naturally disposes of 5% of the drug every​ hour.

We know the formula for exponential rate

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t k D(t) Do (1 100 Where D(t) is the dosage at time t Do is the initial dosage. k is rate constant

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Step 2

Now,

 ...

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t DO) 70 (1-8) 5 D(t) 100 D(t) 70(0.95) So, differentiating on both sides with respect to t, we get D'(t) 70(0.95)(In(0.95)) Now putting t 5 in D'(t), we get D'(5) 70(0.95)5(In(0.95)) D'(5) 2.778 Here negative sign indicates decreasing

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Tagged in

Math

Calculus

Derivative