While receiving mechanical ventilation, a 57-year-old man contracts pneumonia caused by Pseudomonas aeruginosa. The patient is given antibiotic therapy with ceftazidime and gentamicin. Assuming the half-life of gentamicin is 3 hours in this paicular patient, what percentage of the initial dose will most likely remain in his body 6 hours later?

The half-life of a medication is the time required for one-half the total amount of the medication to be excreted from the body. For any given first-order elimination process, 50% of the initial amount of drug is eliminated at the end of the first half-life, 50% of the remaining amount of drug in the body is eliminated at the end of the second half-life, and so on. Therefore, after 3 hours 50% of the gentamicin will be remaining in the body. After another 3 hours (6 hours total), 50% of the remaining 50% will be eliminated. In other words, after 6 hours, 75% of the gentamicin will be eliminated, and 25% of the initial dose will remain. Ref: Buxton I.L., Benet L.Z. (2011). Chapter 2. Pharmacokinetics: The Dynamics of Drug Absorption, Distribution, Metabolism, and Elimination. In L.L. Brunton, B.A. Chabner, B.C. Knollmann (Eds), Goodman & Gilman's The Pharmacological Basis of Therapeutics, 12e.