For a drug that has an initial plasma concentration of 120 mg/L and a half-life of 3 hours, what would the plasma concentration be 12 hours after the initial concentration? A. 15 mg/L B. 112.5 C. 7.5 mg/L D. 60
To calculate the plasma concentration 12 hours after the initial concentration, we need to determine how many half-lives have passed during that time.
The half-life of the drug is given as 3 hours. Therefore, the number of half-lives in 12 hours can be calculated as follows:
Number of half-lives = (time elapsed) / (half-life)
Number of half-lives = 12 hours / 3 hours
Number of half-lives = 4
Each half-life reduces the concentration by half. Therefore, after 4 half-lives, the plasma concentration would be:
Plasma concentration = (initial concentration) / (2 ^ number of half-lives)
Plasma concentration = 120 mg/L / (2^4)
Plasma concentration = 120 mg/L / 16
Plasma concentration = 7.5 mg/L
Therefore, the plasma concentration 12 hours after the initial concentration would be 7.5 mg/L.
The correct answer is C. 7.5 mg/L.
To calculate the plasma concentration 12 hours after the initial concentration, we need to determine how many half-lives have passed.
Given that the half-life is 3 hours, we divide the time elapsed (12 hours) by the half-life to get the number of half-lives: 12 hours / 3 hours = 4 half-lives.
Next, we need to determine the remaining concentration after 4 half-lives. The formula for calculating remaining concentration after a certain number of half-lives is:
remaining concentration = initial concentration * (0.5)^(number of half-lives)
Plugging in the values, we get:
remaining concentration = 120 mg/L * (0.5)^4
= 120 mg/L * (0.0625)
= 7.5 mg/L
Therefore, the plasma concentration 12 hours after the initial concentration is 7.5 mg/L.
The correct answer is C. 7.5 mg/L.