A patient is given a dosage Q mg/ml of a drug at regular intervals of time T hours. Assume that the drug enters the system immediately upon ingestion and that the decrease in the concentration in the blood over time is proportional to the concentration itself with decay rate k. If a residual level above H is unsafe and below L is ineffective, find a dose schedule T for safe and effective concentration.

a) If the first dose is administered at , find the amount remaining in the blood at time T. This is known as the residual, R1 .

Any help would be much appreciated!

Question

A patient is given a dosage Q mg/ml of a drug at regular intervals of time T hours.  Assume that the drug enters the system immediately upon ingestion and that the decrease in the concentration in the blood over time is proportional to the concentration itself  with decay rate k. If a residual level above H is unsafe and below L is ineffective, find a dose schedule T for safe and effective concentration. 

a)	If the first dose is administered at  , find the amount remaining in the blood at time T.   This is known as the residual, R1 . 

Any help would be much appreciated!