Digoxin is used in the treatment of heart disease. Doctors must prescribe an amount of medicine that keeps the concentration of digoxin in the bloodstream above an effective level without exceeding a safe level (there is variation among patients). For an initial dosage of 0.5 mg in the bloodstream, Table 1.2 shows the amount a_n remaining in the bloodstream, Table 1.2 shows the amount of digoxin a_n remaining in the bloodstream of a particular patient after n days, together with the change ∆a_n each day.