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Assuming you take $\pu{200mg}$ of caffeine, it's half life is roughly 6 hours. So after 6 hours there should still be $\pu{100mg}$ of caffeine in your body.

Then why is it generally said that after six hours caffeine's effect should wear off? Shouldn't it only be diminished since there is still $\pu{100mg}$ of caffeine in your body?

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    $\begingroup$ You should probably ask this on Biology.SE I think. Probably not many chemists know the exact mechanism by which caffeine stimulates the human body to know why the effects wear off over time (I certainly don't). My guess is that it has something to do with diminished signaling of some hormone (?) that doesn't signal linearly with concentration of caffeine. $\endgroup$ – jheindel Nov 3 '16 at 23:20
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    $\begingroup$ Perhaps see the caffeine wikipedia page, and read the sections titled pharmacokinetics and pharmacodynamics. These contain the information needed probably, but understanding that information to be able to answer your question is beyond me. $\endgroup$ – jheindel Nov 3 '16 at 23:25

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