Caffeine takes a certain amount of time to work through your system. One study some years ago showed that the half-life of caffeine in healthy adults is 5.7 hours (see source: Half Life of Caffeine). This means if you consume 200 mg of caffeine at mid-day, you would still have 100 mg in you at around 5:45 pm.
a) One fluid ounce of espresso has 64 mg of caffeine. If Daniel drank an espresso at 8:00 am, when will he have 32 mg of caffeine? How many mg of caffeine will he have at noon? How many mg of caffeine will he have at 8:00 pm? How many mg of caffeine will he have at 2 am the next morning?
b) Find an algebraic equation for the amount of caffeine in your system at any given time.