The antibiotic clarithromycin is eliminated from the body according to the formula
[tex]A(t) = 500e^{-0.1386t}[/tex]
where A is the amount remaining in the body (in milligrams) t hours after the drug reaches peak concentration
We need to find the time 't' when amount of drug is reduced to 100
Plug in 100 for A(t) and solve for t
[tex]100 = 500e^{-0.1386t}[/tex]
Divide both sides by 500
[tex]\frac{1}{5} = e^{-0.1386t}[/tex]
Take ln on both sides
[tex]ln(\frac{1}{5}) = ln(e^{-0.1386t})[/tex]
[tex]ln(\frac{1}{5}) = -0.1386tln(e)[/tex]
[tex]ln(\frac{1}{5}) = -0.1386t[/tex]
divide both sides by -0.1386
t = 11.6121
11.61 hours will pass before the amount of drug in the body is reduced to 100.
