It’s ~6 hours. A person takes in 200mg at 6:00 each morning. They have 12.5mg in their system at 6:00 the next morning. The cycle continues. Each morning, they take in 200mg of caffeine and have more caffeine in their system than the day before until they have thousands of mgs of caffeine in their system. Yes?
In: Biology
(editing in progress. I used the wrong half life)
You’re talking about what’s known as an infinite series in math (assuming you drink coffee forever. IN this case it’s:
200 * (1 + 1/8 + 1/64 + 1/512 + ….)
Infinite series come in two flavors: convergent and nonconvergent. A convergent infinite series (which this one is) will not grow infinitely, but instead converge on a finite number.
In this case you’ll finish your coffee each morning with an amount of caffeine in your system that will get closer and closer to 228.571mg. So while caffeine accumulates, it doesn’t do so infinitely. In fact, you end up with not that much more than the first day.
Of course, this is an idealized case ignores the real world problems that the halflife probably depends on a lot of things (possibly even including how much caffeine is in your system), and the amount of caffeine in a cup is going to vary from day to day, etc.
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