Aspirin is metabolized by the body at a rate proportional to its concentration. The half life of aspirin is about 10 hours in a normal person. As aspirin inhibits the clotting of blood it is used systemically on patients with cardiovascular problems, however it should not be taken before surgery. If the surgeon wants no more than 5% of the normal daily dose to be in the blood before surgery, how long should he tell the patient to stop taking aspirin before the surgical procedure? When intake is restarted, how long will it take for the concentration to reach 75% of normal?
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Equation for exponential: At = Aoe^kt and for half life,
At = Ao/2 = Aoe^10k
k = a constant for aspirin, Ao = amount of aspirin at time 0, At = amount at time t.
this gives
1/2 =e^10k
ln(1/2) = 10k
(ln(1/2))/10 = k
-0.0693 = k
At = Ao/20 = Aoe^-0.0693t
1/20 = e^-0.0693t
ln(1/20) = -0.0693t
(ln(1/20))/0.0693 = -t
43.228 = t
So the amount of aspirin drops to 5% of initial value after 43.228 hours
At = 0.75Ao = 1/20Aoe^-0.0693t
(0.75/1/20) =e^-0.0693t
15 =e^-0.0693t
ln(15) = -0.0693t
(ln15)//0.0693 = t
39.07 = t
So the amount of aspirin will reach 75% from 5% in 39.07 hours
At = Ao/2 = Aoe^10k
k = a constant for aspirin, Ao = amount of aspirin at time 0, At = amount at time t.
this gives
1/2 =e^10k
ln(1/2) = 10k
(ln(1/2))/10 = k
-0.0693 = k
At = Ao/20 = Aoe^-0.0693t
1/20 = e^-0.0693t
ln(1/20) = -0.0693t
(ln(1/20))/0.0693 = -t
43.228 = t
So the amount of aspirin drops to 5% of initial value after 43.228 hours
At = 0.75Ao = 1/20Aoe^-0.0693t
(0.75/1/20) =e^-0.0693t
15 =e^-0.0693t
ln(15) = -0.0693t
(ln15)//0.0693 = t
39.07 = t
So the amount of aspirin will reach 75% from 5% in 39.07 hours
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normal digestion is one hour. aspren brack down a half hour.