document.write( "Question 319086: A box contains a radioactive substance. The number of kilograms r(t) at time t years is given by the formula r(t) = 2^-0.002149t. How long will it take until only one-half kilogram of the radioactive substance is left in the box? \n" ); document.write( "

Algebra.Com's Answer #228410 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"r%28t%29+=+2%5E%28-0.002149t%29\"$
\n" ); document.write( "Find t so that,
\n" ); document.write( " $\"2%5E%28-0.002149t%29=0.5\"$
\n" ); document.write( " $\"-0.002149t=log%282%2C%28%280.5%29%29%29\"$
\n" ); document.write( " $\"t=log%282%2C%28%280.5%29%29%29%2F%28-0.002149%29\"$
\n" ); document.write( " $\"t=%28log%28%280.5%29%29%2Flog%28%282%29%29%29%2A%281%2F%28-0.002149%29%29\"$
\n" ); document.write( " $\"t=%28%28-0.301%29%2F%280.301%29%29%2A%281%2F%28-0.002149%29%29\"$
\n" ); document.write( " $\"t=465\"$ years
\n" ); document.write( " \n" ); document.write( "

\n" );