document.write( "Question 275217: to the nearest full day determine how long it will take for 400 millicuries of I-131, which has a half life of 8 days, to decay to 3.125 millicuries? \n" ); document.write( "

Algebra.Com's Answer #200837 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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to the nearest full day determine how long it will take for 400 millicuries of I-131, which has a half life of 8 days, to decay to 3.125 millicuries?
\n" ); document.write( ":
\n" ); document.write( "The half-life equation Ao*2^(-t/h) = A
\n" ); document.write( "Where
\n" ); document.write( "A = resulting amt
\n" ); document.write( "Ao = initial amt
\n" ); document.write( "t = time (in days in this application)
\n" ); document.write( "h = half-life of the substance
\n" ); document.write( ":
\n" ); document.write( "400 * 2^(-t/8) = 3.125
\n" ); document.write( "Divide both sides by 400
\n" ); document.write( "2^(-t/8) = $\"3.125%2F400\"$
\n" ); document.write( "2^(-t/8) = .0078125
\n" ); document.write( ":
\n" ); document.write( "ln(2^(-t/8)) = ln(.0078125)
\n" ); document.write( ":
\n" ); document.write( " $\"-t%2F8\"$ *ln(2) = ln(.0078125)
\n" ); document.write( " $\"-t%2F8\"$ = $\"%28ln%28.0078125%29%29%2F%28ln%282%29%29\"$ ; enter in your calc
\n" ); document.write( " $\"-t%2F8\"$ = -7
\n" ); document.write( "t = -7 * -8
\n" ); document.write( "t = 56 days
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check this on a calc: enter 400 * 2^(-56/7) results: 3.125
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