A drug is administered every 12 hours in doses of 10mg. The drug is neutralized at...

Transcribed Image Text:

A drug is administered every 12 hours in doses of 10mg. The drug is neutralized at an exponential rate of k=0.2. Not all of the drug is neutralized before the next dose is administered. The amount of this "residual drug" in the patient's system at the end of the nth dosing period is given by: R(n) = 10(e-2.4)+ 10(e-2.4)2 +...+ 10(e-2.4)n What is the closed form of this series? 1 - (e-2.4)n 1 e-2.4 10- 10 e- 2-2.4 1 - (e-2.4)n 1 e-2.4 10 e-2.4 (e-24) i=1 n-1 10 e-2.4(e-2.4)i-1 i=1 10 e-24 (e-24)i -1 i=1 10 e-2.4 1 - (e-24)n-1 1 - e-2.4 n 10 (e-24) i=1 10 e -2.4 1- (e-2.4)n-1 e-2.4 1 n-1 10e-24 (e-24)i i=1 10 e-24 1 - (e-2.4)n e-2.4 1 A drug is administered every 12 hours in doses of 10mg. The drug is neutralized at an exponential rate of k=0.2. Not all of the drug is neutralized before the next dose is administered. The amount of this "residual drug" in the patient's system at the end of the nth dosing period is given by: R(n) = 10(e-2.4)+ 10(e-2.4)2 +...+ 10(e-2.4)n What is the closed form of this series? 1 - (e-2.4)n 1 e-2.4 10- 10 e- 2-2.4 1 - (e-2.4)n 1 e-2.4 10 e-2.4 (e-24) i=1 n-1 10 e-2.4(e-2.4)i-1 i=1 10 e-24 (e-24)i -1 i=1 10 e-2.4 1 - (e-24)n-1 1 - e-2.4 n 10 (e-24) i=1 10 e -2.4 1- (e-2.4)n-1 e-2.4 1 n-1 10e-24 (e-24)i i=1 10 e-24 1 - (e-2.4)n e-2.4 1