document.write( "Question 1157177: Carbon-14 has a half-life of 5,730 years. A fossil is found that has 26% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year.) \n" ); document.write( "
Algebra.Com's Answer #779996 by ankor@dixie-net.com(22740)\"\" \"About 
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Carbon-14 has a half-life of 5,730 years.
\n" ); document.write( " A fossil is found that has 26% of the carbon-14 found in a living sample.
\n" ); document.write( " How old is the fossil? (Round your answer to the nearest year.)
\n" ); document.write( ":
\n" ); document.write( "The radioactive decay formula: A = Ao*2^(-t/h) where:
\n" ); document.write( "A = amt after t time
\n" ); document.write( "Ao = initial amt
\n" ); document.write( "t = time of decay
\n" ); document.write( "h = half-life of substance
\n" ); document.write( ":
\n" ); document.write( "let initial amt = 1, resulting amt = .26
\n" ); document.write( "1*2^(t/5730) = .26
\n" ); document.write( "use natural logs
\n" ); document.write( "ln(2^(-t/5730)) = ln(.26)
\n" ); document.write( "log equiv of exponents
\n" ); document.write( "\"-t%2F5730\"ln(2) = ln(.26)
\n" ); document.write( ":
\n" ); document.write( "\"-t%2F5730\"= \"ln%28.26%29%2Fln%282%29\"
\n" ); document.write( "using your calc
\n" ); document.write( "\"-t%2F5730\" = -1.94341
\n" ); document.write( "t = -5730 * -1.94341
\n" ); document.write( "t = 11,136 years
\n" ); document.write( " \n" ); document.write( "
\n" );