The drug lorazepam used to relive anxiety and nervousness ha

The drug lorazepam, used to relive anxiety and nervousness, has a half-life of 14 hours. Its chemical structure is shown in the accompanying figure. If a doctor prescribes one 2.5 milligram tablet every 24 hours, then what percentage of the last dosage remains in the patient’s body when the next dosage is taken?

Solution

decay constatn , k = 0.693/half life = 0.693/14 = 0.0495

Expoenetial decay equation:    N(t) = Noe^(-kt) where No is intial amt

N(t) = 2.5e^(-0.0495*24) = 2.5*0.3 = 0.75 gms

Percentage remaining = (0.75/2.5)*100 = 30%