document.write( "Question 1143674: The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only
\n" ); document.write( "76% of the carbon-14 expected in living matter, when did the tree die? \n" ); document.write( "

Algebra.Com's Answer #764550 by ikleyn(52832) $\"\"$ $\"About$

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document.write( "An equation of the radioactive decay in this case is \r\n" );
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document.write( "     = ,\r\n" );
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document.write( "where C is the initial mass of carbon-14 in the sample; t is the time in years.\r\n" );
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document.write( "Simplify and solve for \"t\", which is the major unknown in this case.\r\n" );
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document.write( "Start canceling \"C\" in both sides.\r\n" );
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document.write( "     = 0.76\r\n" );
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document.write( "Take logarithm base 2 from both sides\r\n" );
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document.write( "    -t/5600 = \r\n" );
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document.write( "    -t/5600 = -0.39593\r\n" );
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document.write( "    t = 5600*0.39593 = 2217 years.      ANSWER\r\n" );
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