   Chapter 11.2, Problem 69E

Chapter
Section
Textbook Problem

# A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each tablet is taken, 20% of the drug remains in the body. (a) How much of the drug is in the body just after the second tablet is taker ? After the third tablet? (b) If Qn is the quantity of the antibiotic in the body just after the nth tablet is taken, find an equation that expresses Qn +1 is terms of Qn. (c) What quantity of the antibiotic remains in the body in the long run?

(a)

To determine

To find: The quantity of the drug in the body after the intake of the second tablet and the third tablet.

Explanation

The quantity of the drug in the body after the intake of first tablet is Q1=100-mg.

The quantity of the drug in the body after the intake of second tablet is,

Q2=100+(20% of the first 100-mg tablet)=100+(20100×100)=100+20=120

Therefore, the quantity of the drug in the body after the intake of second tablet is 120-mg

(b)

To determine

To find: The equation Qn+1 in terms of Qn.

(c)

To determine

To find: The quantity of the antibiotic remains in the body in the long run (limnQn).

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