Warfarin is an anticoagulant that prevents blood clotting; often it is prescribed to stroke victims in order to help ensure blood flow. The level of warfarin has to reach a certain concentration in the blood in order to be effective.

Suppose warfarin is taken by a particular patient in a 5 mg dose each day. The drug is absorbed by the body and some is excreted from the system between doses. Assume that at the end of a 24 hour period, 8% of the drug remains in the body. Let $Q(n)$ be the amount (in mg) of warfarin in the body before the $(n + 1)$st dose of the drug is administered. Complete the following table.

$Q(1) = 5\left(\frac{8}{100}\right)$ mg
$Q(2) = 5\left(\frac{8}{100}\right)\left(1 + \frac{8}{100} \right)$ mg
$Q(3) = 5\left(\frac{8}{100}\right)\left(1 + \frac{8}{100} + \left(\frac{8}{100}\right)^2 \right)$ mg
$Q(4) = 5\left(\frac{8}{100}\right)\left(1 + \frac{8}{100} + \left(\frac{8}{100}\right)^2 + \left(\frac{8}{100}\right)^3 \right)$ mg
$Q(5) =$ mg
$Q(6) =$ mg
$Q(7) =$ mg
$Q(8) =$ mg
$Q(9) =$ mg
$Q(10) =$ mg

Based on this data, estimate the long term amount of warfarin in the body:

$\displaystyle{\lim_{n \rightarrow \infty} Q(n) = }$ mg