After a dose is swallowed, caffeine is absorbed across the gut into the bloodstream with little first-pass loss, so the plasma concentration climbs steeply and peaks about 30–60 minutes later. That peak is the moment of maximal receptor occupancy and usually the strongest subjective alertness. From there the curve falls because the liver is removing caffeine, and the removal is first-order: the rate of elimination is proportional to how much caffeine is present, so a constant fraction is cleared per unit time rather than a constant amount.
That property is what makes the half-life useful. The half-life \(t_{1/2}\) is the time required for the plasma concentration to fall to half its current value. In most healthy adults caffeine's \(t_{1/2}\) is roughly 3–7 hours, so a level of 100% becomes 50% after one half-life, 25% after two, and 12.5% after three. The decline is exponential:
\[ C(t) = C_0 \cdot \left(\frac{1}{2}\right)^{t/t_{1/2}} \]
where \(C_0\) is the peak concentration, \(t\) is time since the peak, and \(t_{1/2}\) is the half-life. The liver enzyme CYP1A2 (cytochrome P450 1A2) performs most of this work, converting caffeine into paraxanthine, theobromine, and theophylline, which are then further metabolized and excreted.
Because the antagonism at A1 and A2A receptors is competitive, alertness tracks the caffeine concentration rather than staying flat until the drug vanishes. As the curve descends, adenosine — which has been accumulating the whole time — increasingly outcompetes the dwindling caffeine for the receptor, so the blockade weakens gradually and sleepiness returns well before caffeine is fully gone.