Question 149823
{{{L = D/(1-(0.5)^(n/h))}}}
where D is the amount taken every n hours and H is the drug’s half-life in hours.
(1) If 2.5 milligrams of Lorazepam with a half-life of 14 hours is taken every 24 hours, then to what level does the drug build up over time?
{{{L = D/(1-(0.5)^(n/h))}}}
{{{L = 2.5mg/(1-(0.5)^(24/14))}}}
{{{L = 2.5mg/(1-(0.5)^(1.714))}}}
{{{L = 2.5mg/(1-0.3048)}}}
{{{L = 2.5mg/(0.6952)}}}
{{{L = 3.59mg}}}


(2)   If a doctor wants the level of Lorazepam to build up to a level of 5.58 milligrams in a patient taking 2.5 milligram doses, then how often should the doses be taken?
{{{L = D/(1-(0.5)^(n/h))}}}
{{{5.58mg = 2.5mg/(1-(0.5)^(n/14))}}}
{{{(1-(0.5)^(n/14)) = 2.5/5.58}}}
{{{-(0.5)^(n/14)= -0.552}}}
{{{log((0.5)^(n/14)) = log(0.552)}}}
{{{(n/14) * log(0.5) = -0.258}}}
{{{(n/14) * (-0.301) = -0.258}}}
{{{n/14 = 0.857}}}
{{{n = 0.857*14}}}
{{{n = 12}}}

(3)   What is the difference between taking 2.5 milligrams of Lorazepam every 12 hours and taking 5 milligrams every 24 hours? 
{{{L = D/(1-(0.5)^(n/h))}}}
{{{L = 2.5mg/(1-(0.5)^(12/14))}}}
{{{L = 5.58mg}}}

{{{L = D/(1-(0.5)^(n/h))}}}
{{{L = 5/(1-(0.5)^(24/14))}}}
{{{L =5mg/(0.6952)}}}
{{{L = 7.19mg}}}

Big difference