If a drug has a half life of, let say 72 hours, and you take it every day, how do the levels not continuously climb?
In: Biology
Because you’re adding a fixed amount of the drug every day, but progressively larger *amounts* are decaying (since a constant *fraction* goes away at a fixed interval). Eventually you hit an equilibrium.
Imagine you have a very large leaky bucket. Every hour, half of *whatever amount* is in the bucket will leak out. If you fill it 1/4, 1/8 will be gone in an hour. If you fill it to 1/2, 1/4 will be gone.
So let’s say every hour you add 1/4 to the empty bucket.
Hour 1: You add 1/4, bucket goes from empty to 1/4 full.
Hour 2: You add 1/4, 1/8 leaked out, you now have 3/8.
Hour 3: You add 1/4, 3/16 leaked out, so you now have 7/16.
Hour 4: You add 1/4, 7/32 leaked out, you have now 15/32.
Every hour you have seen larger amounts leak out, 1/8 < 3/16 < 7/32 … getting closer and closer to 1/4. At the same time, you’re seeing the height of the water in the bucket slow down, going from 0 -> 1/4 -> 3/8 -> 7/16 -> … -> 1/2.
Eventually, when the bucket is 1/2 full, you walk away and come back and find 1/4. You add another 1/4, walk away, come back and find 1/4 again. That’s your equilibrium.
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