A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each tablet is taken, 20% of the drug present in the preceding time step 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 Qn is the quantity of the antibiotic in the body justafter the nth tablet is taken, write a difference equationthat expresses Qn+1 in terms of Qn. (c) Find a formula for Qn as a function of n. (d) What quantity of the antibiotic remains in the body inthe long run?
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A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each tablet is taken, 20% of the drug present in the preceding time step 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 Qn is the quantity of the antibiotic in the body just
after the nth tablet is taken, write a difference equation
that expresses Qn+1 in terms of Qn.
(c) Find a formula for Qn as a function of n.
(d) What quantity of the antibiotic remains in the body in
the long run?
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