document.write( "Question 298119: The half-life of a substance is the time it takes for half of the substance to remain after natural decay. Radioactive water (tritium) has a half-life of 12.6 years. How long will it take for 85% of a sample to decay? \n" ); document.write( "

Algebra.Com's Answer #214593 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The half-life of a substance is the time it takes for half of the substance to remain after natural decay.
\n" ); document.write( "Radioactive water (tritium) has a half-life of 12.6 years.
\n" ); document.write( "How long will it take for 85% of a sample to decay?
\n" ); document.write( ":
\n" ); document.write( "The half-life formula: A = Ao*2^(-t/h)
\n" ); document.write( "Where
\n" ); document.write( "A = resulting amt after t time
\n" ); document.write( "Ao = initial amt
\n" ); document.write( "h = half-life of the substance
\n" ); document.write( "t = time
\n" ); document.write( ":
\n" ); document.write( "If we start with 1 unit, after 85% has decayed we will have .15 units left (A)
\n" ); document.write( ":
\n" ); document.write( "1*2^(-t/12.6) = .15
\n" ); document.write( "using nat log
\n" ); document.write( "ln(2^(-t/12.6)) = ln(.15)
\n" ); document.write( "log equiv of exponents
\n" ); document.write( " $\"-t%2F12.6\"$ *ln(2) = ln(.15)
\n" ); document.write( ":
\n" ); document.write( " $\"-t%2F12.6\"$ *.693 = =1.897
\n" ); document.write( ":
\n" ); document.write( " $\"-t%2F12.6\"$ = $\"-1.897%2F.693\"$
\n" ); document.write( ":
\n" ); document.write( " $\"-t%2F12.6\"$ = -2.737
\n" ); document.write( "Multiply both sides by -12
\n" ); document.write( "t = -2.737 * -12
\n" ); document.write( "t = 34.5 years for 85 % to decay
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check on your calc: enter: 2^(-34.5/12.6) should =.14988 ~ .15
\n" ); document.write( " \n" ); document.write( "

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