Okay, this question straddles math, physics, biology, and chemistry, so I'm not sure if this is the correct forum to post it in, but I was using mostly chemistry knowledge to solve it, so I would guess that may be the correct method. Anyway, it's not homework, but it is similar to many homework problems, so mods, if you want to move the topic, no problem. Here is the problem: A person (me actually) takes a certain drug 3 times a day. He takes 10 mg of this drug at 8am, 10 mg at 2pm, and 10mg at 8pm. This drug has a half life of 4 hours. My question is, is it possible to solve for whether the quantity of the drug in the blood stream will approach a stable quantity, or at least fluctuate between certain boundaries? So the doses look like this: 10mg -- 6 hrs --- 10 mg -- 6 hrs --10 mg -- 12 hrs, repeat Here is the work I have done so far: With a half life of 4 hours, the drug decays to 35.3 % during the two 6 hour breaks between doses. It decays to 12.5% during the 12 hour break between doses. I'm thinking that I may be able to solve this with a series, and then using an integral test to see if the quantity converges, but the problem is that the pattern is inconsistent. Then I considered trying to solve the problem with multiple series (one for each time break) but obviously since each series is dependent on all of the half-lives, this would also be problematic. I also tried just working out a few times by hand to see what happens. The first few quantities are: 10mg 3.53mg 4.78mg 1.81mg 4.17mg 5.00mg 1.84mg 4.18mg 5.00mg 1.84mg So it looks like there might be a pattern, but obviously this is no mathematical proof. Any ideas?