The half-life is not a universal constant. It is a property of how fast a given person's liver clears caffeine, and it varies enough that the same cup of coffee can act for a few hours in one person and most of a day in another. The concentration curve \(C(t) = C_0 \cdot (1/2)^{t/t_{1/2}}\) makes the consequence explicit: doubling the half-life does not double the duration of a fixed threshold effect — it stretches the whole decay, so the time spent above any given concentration grows roughly in proportion to \(t_{1/2}\).
Several factors move the half-life in predictable directions. Genetic variation in CYP1A2 — the enzyme that performs most of the demethylation — produces fast and slow metabolizer phenotypes. Pregnancy, especially in the third trimester, slows clearance substantially. Oral contraceptives and some drugs that inhibit CYP1A2 (for example, fluvoxamine or ciprofloxacin) also slow it. Liver disease impairs clearance. In the other direction, smoking induces CYP1A2, so smokers clear caffeine faster and may need more of it for the same effect; quitting smoking can therefore make a previously tolerated dose feel much stronger.
Because the effect depends on staying above the concentration needed to hold adenosine off the receptor, any factor that lengthens the half-life also lengthens the window of alertness and pushes more caffeine into the hours before sleep. That is why the same evening coffee can be harmless for one person and disruptive for another.