document.write( "Question 1138573: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17% each hour. To the nearest tenth, what is the half-life of the drug? \n" ); document.write( "

Algebra.Com's Answer #756360 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Since it decays by 17% per hour, the amount remaining gets multiplied by 100-17 = 83% each hour. The amount remaining after t hours is then the initial amount, multiplied by 0.83 t times:

\n" ); document.write( " $\"300%280.83%29%5Et\"$

\n" ); document.write( "The problem asks for the half-life -- i.e., the amount of time it takes for the original amount to be reduced to half.

\n" ); document.write( " $\"300%280.83%29%5Et+=+150\"$
\n" ); document.write( " $\"0.83%5Et+=+0.5\"$
\n" ); document.write( " $\"t%2Alog%28%280.83%29%29+=+log%28%280.5%29%29\"$
\n" ); document.write( " $\"t+=+log%28%280.5%29%29%2Flog%28%280.83%29%29\"$

\n" ); document.write( "Use a calculator.... \n" ); document.write( "

\n" );