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
using that math, never.
After 12 days of this you wake up with 13 and 1/3rd mg of caffeine in your system, add 200mg brings you up to 213 + 1/3mg of caffeine (640/3), divide that by 16 (4 half-lives) and you get 40/3, or 13+1/3, the amount you started the day with. after that, the total amount will not increase
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