![]() This means if you consume 200 mg of caffeine at mid-day, you would still have 100 mg in you at around 5:45 pm. One study showed that the half-life of caffeine in healthy adults is 5.7 hours ( see source ). N(t) = N_1\left(\frac $ which in this case is quite near to the mid hour. Caffeine is no different and takes a certain amount of time to work through your system and be metabolized by your liver. That is, the amount of coffee $N(t)$ for $t > 1$, is given by ![]() Then the amount of coffee left in your system, $t$ hours after you started drinking the coffee will be exactly what you already have in your question except the starting amount will be $N_1$ and you will subtract $1$ from the time in the function to account for the hour passed. Let $N_1$ be the amount of coffee in your system at $t = 1$ hours (when you are done drinking it). We split the time up into two cases: the first hour from when you begin drinking the coffee and then the rest of the time.
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