Final answer:
To calculate the remaining medication at 6:00pm with a half-life of 5.5 hours from an initial dose of 10 milligrams, apply the formula for exponential decay. Approximately 4.74 milligrams would be left after 6 hours, slightly more than one half-life.
Step-by-step explanation:
The question asks for the amount of medication remaining in a patient's blood after a certain time given the drug's half-life. To calculate the remaining dose of an exponentially eliminated medication after a specific duration, we use the formula:
Remaining amount = Initial dose × (1/2)^(Time elapsed/Half-life).
In this scenario, the initial dose (10 milligrams) is administered, and we want to determine the milligram amount left after 6 hours, with a half-life of 5.5 hours. Since half-life is the time it takes for half of the drug to be eliminated, after one half-life (5.5 hours), there will be half of the initial dose remaining.
However, the period in question here is 6 hours, which is slightly over one half-life, so we would perform the calculation as follows:
- Time elapsed = 6.0 hours
- Half-life = 5.5 hours
- Remaining amount = 10 mg × (1/2)^(6/5.5)
Final calculation:
Remaining amount = 10 mg × (1/2)^(1.0909) ≈ 10 mg × 0.474
Remaining amount ≈ 4.74 mg.
Therefore, approximately 4.74 milligrams of the medication would remain in the patient's bloodstream at 6:00pm.