document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #308230 by nerdybill(7384) $\"\"$ $\"About$

You can put this solution on YOUR website!
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?
\n" ); document.write( ".
\n" ); document.write( "set f(x) to 2 and solve for x:
\n" ); document.write( " $\"2+=+40%280.8%29%5Ex\"$
\n" ); document.write( " $\"2%2F40+=+%280.8%29%5Ex\"$
\n" ); document.write( "take log base .8 of both sides:
\n" ); document.write( " $\"log%280.8%2C2%2F40%29+=+x\"$
\n" ); document.write( "change of base:
\n" ); document.write( " $\"log%282%2F40%29%2Flog%280.8%29+=+x\"$
\n" ); document.write( " $\"13.43+=+x\"$
\n" ); document.write( "answer:
\n" ); document.write( "more than 13.43 hours \n" ); document.write( "

\n" );