Assume the half-life of a certain drug is 8 hours and 50o mg of that drug was gi

Question

Assume the half-life of a certain drug is 8 hours and 50o mg of that drug was given as a treatment. Ca Fill in the table below. Hours after Amount of drug taking drug in system 16 24

Explanation / Answer

Dear Student Thank you for using Chegg !! Given that half life of drug is 8 hours And initial quantity (P0) = 500 mg P = P0 (e)^ -kt P := Quantity of drug at any time t P0:- Initial Quantity k :- Rate of increase t:- Time elapsed in hours Now after 8 hours quantity reduces to half i.e. P0/2 => P0/2 = P0 e^-8k 1/2 = e^-8k Taking natural log both sides ln(0.5) = -8k -0.6931472 = -8k k = 0.086643398 P = 500e^(-0.0866t) Hours Amount of Drug 0 500e^(-0.0866*0) = 500 8 500e^(-0.0866*8) = 250 16 500e^(-0.0866*16) = 125 24 500e^(-0.0866*24) = 62.5 b) Amount of drug t hours after taking 500 mg P = 500e^(-0.0866t) c) Time elapsed when remaining drug amount is 5 mg 5 = 500e^(-0.0866t) 0.01 = e^(-0.0866t) Taking natural log both sides -4.6051702 = -0.0866t t = 53.15084952 hours Solution

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