document.write( "Question 173139: a chunk of radioactive material decays from a mass of 450 grams to 165 grams in two weeks,(14 days). find the half life time and the amount of material left after 70 days \n" ); document.write( "

Algebra.Com's Answer #128011 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!
a chunk of radioactive material decays from a mass
\n" ); document.write( "of 450 grams to 165 grams in two weeks,(14 days).
\n" ); document.write( "

\r\n" );
document.write( "The exponential equation to use is:\r\n" );
document.write( ", where\r\n" );
document.write( " = Amount, in grams\r\n" );
document.write( " = time, in days\r\n" );
document.write( " = a constant\r\n" );
document.write( " = a constant\r\n" );
document.write( "\r\n" );
document.write( "When  days,  grams, therefore\r\n" );
document.write( "(,) = (,) is a point on the graph.\r\n" );
document.write( "\r\n" );
document.write( "When  days,  grams, therefore \r\n" );
document.write( "(,) = (,) is another point on the graph.\r\n" );
document.write( " \r\n" );
document.write( "Substitute the first point in the equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have found that P is the original amount\r\n" );
document.write( "Substitute the second point in the equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 450:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use the fact that  is equivalent to \r\n" );
document.write( "to rewrite the equation in natural log form:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 14\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Get your calculator and find the right side:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute  for  in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we can do the last two parts:\r\n" );
document.write( "

\n" ); document.write( ">>...find the half life time...<<
\n" ); document.write( "

\r\n" );
document.write( "This asks us to find the time it takes\r\n" );
document.write( "for the original 450 grams to reduce to\r\n" );
document.write( "just half of that amount or 225 grams\r\n" );
document.write( "(half of 450 grams)\r\n" );
document.write( "\r\n" );
document.write( "So we substitute 225 for A in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 450:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Again use the fact that  is equivalent to \r\n" );
document.write( " to rewrite the equation in natural \r\n" );
document.write( "log form:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "divide both sides by \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Get your calculator and find the right side:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, it takes about 9.7 days for the radioactive\r\n" );
document.write( "material to reduce from its original amount\r\n" );
document.write( "of 450 grams to half its original amount, or\r\n" );
document.write( "225 grams.\r\n" );
document.write( "\r\n" );
document.write( "Now the last part:\r\n" );
document.write( "

\n" ); document.write( ">>...and the amount of material left after 70 days...<<
\n" ); document.write( "

\r\n" );
document.write( "All we have to do is substitute 70 for t in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So after 70 days, there is only about 3 grams\r\n" );
document.write( "remaining.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );