Problem 69E

69. 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 taken? After the third tablet?

(b) If $Q_{n}$ is the quantity of the antibiotic in the body just after the $n$ th tablet is taken, find an equation that expresses $Q_{n+1}$ in terms of $Q_{n}$.

(c) What quantity of the antibiotic remains in the body in the long run?

Step-by-Step Solution