Two 5-grain aspirin tablets contain 650 mg of the drug. With aspirins half-life of 29 minutes, how much is left in the bloodstream after 2 hours? How long does it take for the level to be equivalent to 10 mg of aspirin? If an individual takes two tablets every 4 hours, what is the maintenance level of the aspirin?

Question

Steve · Answer

the fraction left after t minutes is

(1/2)^(t/29)

so, after two hours (120 minutes), the fraction left is

1/2^(120/29) = 0.0568

To find how log it takes to get to 10mg,

650(1/2)^(t/29) = 10
(1/2)^(t/29) = 1/65
t/29 = log(1/65)/log(1/2) = 6.022
t = 174.65
or, almost 3 hours

After 4 hours, the fraction left is
(1/2)^(240/29) = 0.00323

So, over the long term, the amount left is

650(.00323 + .00323^2 + ...)
= 2.1 mg

Will · Answer

so the maintenance level is 2.1 mg?