Final answer:
Half-life is the time it takes for a substance's concentration to decrease to half its initial value. For caffeine with a 6-hour half-life, in 6 hours the amount falls to 50 mg, in 12 hours to 25 mg, and in 18 hours to 12.5 mg when starting from 100 mg.
Step-by-step explanation:
The concept of half-life is essential when calculating the amount of a substance that remains after a certain period of time. For substances like caffeine that exhibit exponential decay in the human body, the half-life is the duration it takes for the substance's concentration to decrease to half of its initial value. As it pertains to your question, caffeine has a half-life of approximately 6 hours in humans.
In practical terms, if you start with a certain amount of caffeine, after one half-life (6 hours), you will have half of that amount remaining. After two half-lives (12 hours), a quarter of the original amount will remain because half of the previous half-life's amount will have decayed. And after three half-lives (18 hours), you will have one-eighth of the initial amount since half of the amount from the second half-life decays again.
For example, with an initial caffeine concentration of 100 mg:
After 6 hours: 50% of 100 mg = 50.0 mg
After 12 hours: 50% of 50 mg = 25.0 mg
After 18 hours: 50% of 25 mg = 12.5 mg
These calculations assume that the decay is a first-order kinetic process and that the rate of elimination of caffeine does not change over time.