How long for the caffeine from a typical cup of coffee to leave the system?

[Lobsang]

If I have one cup of coffee all day - How long roughly will it take for the effects of the caffeine on my alertness to be zero?
If I’ve had double the dose of caffeine in that cup - how does that effect the timescale (does it double the amount of time before the effect is zero? Or does it make no difference? Or somewhere inbetween)

[Squink]

Peak plasma caffeine concentration is reached between 15 and 120 min after oral ingestion in humans and equals 8 to 10 mg/l for doses of 5 to 8 mg/kg (Arnaud and Welsch, 1982; Bonati et al., 1982). Ingestion of a single cup of coffee provides a dose of 0.4 to 2.5 mg/kg. It can therefore be estimated that this gives a peak concentration of 0.25 to 2 mg/l or approximately 1 to 10 µM.

For doses lower than 10 mg/kg, caffeine half-lives range from 0.7 to 1.2 h in rat and mouse, 3 to 5 h in monkey (Bonati et al., 1984-1985) and 2.5 to 4.5 h in humans (Arnaud, 1987). There are no differences in caffeine half-life in young and elderly humans (Blanchard and Sawers, 1983b)
…
In adult males, caffeine half-life is reduced by 30 to 50% in smokers compared with nonsmokers (Hart et al., 1976; Joeres et al., 1988; Murphy et al., 1988), whereas it is approximately doubled in women taking oral contraceptives (Patwardhan et al., 1980) and greatly prolonged (up to 15 h) during the last trimester of pregnancy (Aldridge et al., 1981; Knutti et al., 1981; Brazier et al., 1983).

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[Ignatz]

I saw recently in a tv ad for an OTC sleep aid that caffeine ingested after 2 p.m. can affect your sleep. I switched from a caffeinated tes to no-caf one for my evening relaxer and I’ve slept right thru most of the time since then. No cite.