Question

The half-life of caffeine in the human body is 5 hours. Before each class, your instructor consumes approximately 100 mg of caffeine. How much caffeine does the instructor have in their system at the end of one 50-minute lecture?

a) 80 mg
b) 60 mg
c) 40 mg
d) 20 mg

Answer 1

The instructor will have approximately 0.0977 mg of caffeine in their system at the end of one 50-minute lecture.

Step-by-step explanation:

The half-life of caffeine in the human body is 5 hours, which means that after 5 hours, half of the initial amount of caffeine will remain in the body. In this case, the instructor consumes 100 mg of caffeine before each class, so we can calculate the amount of caffeine remaining after one 50-minute lecture.

Since the half-life is 5 hours, we can calculate how many half-lives occur in 50 minutes. There are 10 half-lives in 50 minutes, because 5 minutes is half of 10 minutes, 10 minutes is half of 20 minutes, and so on. This means that after the 50-minute lecture, the instructor will have 1/1024th of the initial 100 mg of caffeine remaining, which is approximately 0.0977 mg.

Therefore, the instructor will have approximately 0.0977 mg of caffeine in their system at the end of one 50-minute lecture.