Models & Qualitative Behavior · Superchallenge problem

A patient takes a $100$ mg dose of a drug every $6$ hours; each dose enters the blood instantly, and between doses the drug is eliminated by $A' = -kA$ with a half-life of $6$ hours. Once the levels have settled into a repeating pattern, what is the average amount of drug in the blood over one dosing period (in mg)? Give an exact answer.