Question

the half-life of a drug in the bloodstream is 8 hours. By what factor does the concentration of the drug decrease in 16 hours?

Answer 1

After 16 hours, which equals two half-lives, the concentration of the drug in the bloodstream decreases by a factor of 1/4.

Step-by-step explanation:

The half-life of a substance is the time it takes for its concentration to reduce to half its initial value. In the context of the question, the drug in question has a half-life of 8 hours, meaning after 8 hours, its concentration decreases to one-half of the original amount. After 16 hours, which is two half-lives, the concentration would reduce by a factor of two twice, or by a factor of four (22).

Using the formula for the concentration after n half-lives:

(1/2)n × initial concentration

For two half-lives, this becomes:

(1/2)2 = 1/4

Thus, after 16 hours, the concentration of the drug in the bloodstream decreases by a factor of 1/4.