A patient is given a dosage Q of a drug at regular intervals of time T . The concentration of the drug in the blood has been shown experimentally to obey the law:

a. If the first dose is administered at t = 0 hr, show that after T hr have elapsed, the residual:

b. Assuming an instantaneous rise in concentration whenever the drug is administered, show that after the second dose and T hr have elapsed again, the residual:

c. Show that the limiting value R of the residual concentrations for doses of Q mg/ml repeated at intervals of T hr is given by the formula:

d. Assuming the drug is ineffective below a concentration L and harmful above some higher concentration H, show that the dose schedule T for a safe and effective concentration of the drug in the blood satisfies the formula: