This is basically a repost to Dr. Math over a week ago where I didn't receive an answer. Maybe they thought it was for homework.
A friend of mine is an internist who is going to carry out some studies where he wants to take extra care not to accumulate certain medicines in the bodies of his patients, eventually poisoning them.
That has happened sometimes with gold salts which have a "half life" of 15 hours. That means, after each 15 hours there is still half of what was there 15 hours ago. So if he gives the patient another dosage after, say, 12 hours, there is still quite a good amount left in the body, but I don't know how much.
The question is, how could he calculate the right amount of medicine to bring the total in the body up the the original level - no more, no less?
The formula should depend on the initial dosage (which will be achieved again with those additional "maintenenace" dosages every so many hours), time elapsed since the last dosage, and the "half time" of the medicine. Only for these gold salts is it 15 hours, but there are others.
I know how to plot this curve, and it seems to be similar to the discharge curve of a capacitor (in electronics), but have no clue how to develop the formula. If somebody could provide me with a simplified version that is easy to convert into an Excel spread sheet, I would appreciate even more.