Final answer:
The half-life of a drug with an elimination rate constant of 0.564 hr-1 can be calculated using the formula t1/2 = 0.693/k, yielding a half-life of approximately 1.23 hours.
Step-by-step explanation:
When considering a drug's elimination from the body, one often looks at the half-life, which refers to the time required for the drug's concentration to reduce to half its initial value. In the context of first-order kinetics, the half-life of a substance can be calculated using the formula t1/2 = 0.693/k, where k is the elimination rate constant. For a drug with an elimination rate constant of 0.564 hr-1, the half-life can be found by rearranging the formula to t1/2 = 0.693/0.564.
Performing the calculation t1/2 = 0.693/0.564 gives a half-life of approximately 1.23 hours. It's crucial to understand the half-life concept, especially in fields like pharmacokinetics where it informs dosing schedules and medication management. The half-life indicates after how much time the drug concentration will be half of its initial amount in the body, provided the elimination process follows first-order kinetics.
Note that the earlier mentioned option C, 1.77 hours, does not correspond to the calculation based on the given rate constant. This highlights the importance of accurately applying the half-life formula in pharmaceutical calculations.