Question

Consider a drug that is taken in 55 mg doses daily. Suppose that the first dose is taken when t = 0, and that t is measured in hours. If the half-life of the drug is 6.7 hours, what fraction of the drug remains in the patient after 24 hours?

a) 1/16
b) 1/8
c) 1/4
d) 1/2

Answer 1

After 24 hours, approximately 1/8 of the drug remains in the patient.

Step-by-step explanation:

The fraction of the drug that remains in the patient after 24 hours can be determined using the concept of half-life. The half-life of the drug is 6.7 hours, which means that after each 6.7 hours, the amount of drug remaining in the patient is reduced by half. To calculate the fraction of the drug remaining after 24 hours, we divide 24 by 6.7 to find the number of half-lives that have passed.

No. of half-lives = 24 / 6.7 = 3.58

Since we can't have a fraction of a half-life, we can consider that after 24 hours, approximately 3 half-lives have passed. Each half-life reduces the amount of drug by half, so after 3 half-lives, the fraction of drug remaining is (1/2) * (1/2) * (1/2) = 1/8.