# The half-life of caffeine

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It’s ~6 hours. A person takes in 200mg at 6:00 each morning. They have 12.5mg in their system at 6:00 the next morning. The cycle continues. Each morning, they take in 200mg of caffeine and have more caffeine in their system than the day before until they have thousands of mgs of caffeine in their system. Yes?

In: Biology

The extra 12.5mg of caffeine also has the same halflife. The next day, it will have reduced to 0.78mg.

Plus the 12.5mg, and another 200 mg, adds up to 213.28mg.  Another day, and the new 12.5mg will have reduced to 0.78mg, and the 0.78mg from the first day will have reduced to 0.05mg.

Your amount of caffeine will never increase towards infinity. Mathematically, it will increase towards (but never quite reaching) some certain value. That value depends on what the halflife time is and how much you are adding each time.

You can visualize it this way: What would happen if you started with 800mg of caffeine in your system, and add 200mg each day?

First day: 1000mg

Second day: The 1000mg has reduced to 62.5mg, + 200mg = 262.5mg

Third day: The 262.5mg has reduced to 16.4mg, +200mg = 216.4mg

As you can see, we are not ending up with more and more caffeine in the system.