Final answer:
The steady state concentration of a drug metabolized by first-order kinetics is typically reached within four to five half-lives, given the constant nature of half-lives in first-order reactions.
Step-by-step explanation:
During continuous infusion of a drug that is metabolized by first-order kinetics, the steady state concentration is reached in approximately four to five half-lives. The half-life is the time required for the concentration of the drug to reach half of its initial value. In a first-order reaction, the half-life is constant and does not depend on the initial concentration of the substance. The half-life of a first-order reaction is demonstrated by the fact that after each half-life interval, the concentration of the reactant decreases by a factor of 2. Therefore, the concentration approaches but never quite reaches zero, and after around four to five half-lives, the concentration will have achieved a relatively constant level, known as the steady state.