Let’s say that I take a drug which has a half-life of 90 hours. Let’s also stipulate that I have been taking one milligram of this substance every day for seven days. How much of this drug is in my body exactly one week (168 hours) after taking the first dose? How do I solve this type of math problem?
I presume that you are about to take the eighth dose, but you have not yet.
I don’t have the math chops to do anything other than brute force it, so beginning from the time you’re about to take dose #2:
[1mg / 2^(168/90) + 1mg / 2^(144/90) + 1mg / 2^(120/90) + 1mg / 2^(96/90) + 1mg / 2^(72/90) + 1mg / 2^(48/90) + 1mg / 2^(24/90)] = 3.5748978mg
Presuming you stay on the drug, by day 19, there will be only about 30mcg left of that original pill, and you should be at a relatively stable 4.8mg.
(How is this drug cleared from the system, btw? Is it fat-soluble [I would presume a water-soluble drug should have a biological half-life of about 24 hours]?)