After 12 hours, what concentration of a drug remains in the system if it has a half-life of 4 hours and the initial dose was 1000 mg?

To determine the concentration of a drug in the system after a certain period, you can use the concept of half-life. The half-life of a drug is the time it takes for the concentration of that drug to be reduced to half its initial value.

In this case, the drug has a half-life of 4 hours, which means every 4 hours, the amount of drug in the system is halved. Starting with an initial dose of 1000 mg, we can calculate the remaining concentration after each half-life:

• After the first 4 hours (1 half-life), the concentration would be:

(1000 , \text{mg} \times \frac{1}{2} = 500 , \text{mg})

• After the second 4 hours (2 half-lives), the concentration would be:

(500 , \text{mg} \times \frac{1}{2} = 250 , \text{mg})

• After the third 4 hours (3 half-lives), the concentration would be:

(250 , \text{mg} \times \frac{1}{2} = 125 , \text{mg})