▁( t = 0 ) ▁K ▁is ▁the ▁elim ination ▁rate ▁constant ▁ ▁Der iv ation ▁ ▁In ▁first - order ▁( linear ) ▁k inet ics , ▁the ▁pl asma ▁concentration ▁of ▁a ▁drug ▁at ▁a ▁given ▁time ▁t ▁ ▁after ▁single ▁do se ▁administration ▁via ▁IV ▁bol us ▁injection ▁is ▁given ▁by ; ▁ ▁where : ▁ ▁C 0 ▁is ▁the ▁initial ▁concentration ▁( at ▁t = 0 ) ▁ ▁t 1 / 2 ▁is ▁the ▁half - life ▁time ▁of ▁the ▁drug , ▁which ▁is ▁the ▁time ▁needed ▁for ▁the ▁pl asma ▁drug ▁concentration ▁to ▁drop ▁to ▁its ▁half ▁ ▁Therefore , ▁the ▁amount ▁of ▁drug ▁present ▁in ▁the ▁body ▁at ▁time ▁t ▁ ▁is ; ▁ ▁where ▁V d ▁is ▁the ▁apparent ▁volume ▁of ▁distribution ▁ ▁Then , ▁the ▁amount ▁elimin ated ▁from ▁the ▁body ▁after ▁time ▁t ▁ ▁is ; ▁ ▁Then , ▁the ▁rate ▁of ▁elim ination ▁at ▁time ▁t ▁is ▁given ▁by ▁the ▁derivative ▁of ▁this ▁function ▁with ▁respect ▁to ▁t ; ▁ ▁And ▁since ▁ ▁is ▁fraction ▁of ▁the ▁drug ▁that ▁is ▁removed ▁per ▁unit ▁time ▁measured ▁at ▁any ▁particular ▁instant , ▁then ▁if ▁we ▁divide ▁the ▁rate ▁of ▁elim ination ▁by ▁the ▁amount ▁of ▁drug ▁in ▁the ▁body ▁at ▁time ▁t , ▁we ▁get ; ▁ ▁References ▁ ▁Category : Ph arm ac ok in etic ▁metrics <0x0A> </s> ▁Hy ung - min , ▁also ▁sp elled ▁H ye ong - min , ▁is ▁a ▁Korean ▁mascul ine ▁given ▁name . ▁Its ▁meaning ▁diff