Question 447792
The function f(x)= 40(0.8)^x gives the amount of a medication in milligrams present in a patient's system x hours after taking a 40-mg dose. In how many hours will there be less than 2 mg of the drug in a patient's system? 
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set f(x) to 2 and solve for x:
{{{2 = 40(0.8)^x}}}
{{{2/40 = (0.8)^x}}}
take log base .8 of both sides:
{{{log(0.8,2/40) = x}}}
change of base:
{{{log(2/40)/log(0.8) = x}}}
{{{13.43 = x}}}
answer:
more than 13.43 hours