document.write( "Question 1189645: When organisms die, the amount of carbon-14 in its system starts to decrease. The carbon-14 is about 6000 years. If a piece of human bone was found to contain only 1/3 of carbon-14 it originally had, how long ago did the human die \n" ); document.write( "

Algebra.Com's Answer #821065 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "When organisms die, the amount of carbon-14 in its system starts to decrease.
\n" ); document.write( "The $\"highlight%28half-life%29\"$ of the carbon-14 is about 6000 years.
\n" ); document.write( "If a piece of human bone was found to contain only 1/3 of carbon-14 it originally had, how long ago did the human die ?
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document.write( "The remaining mass M(t) of Carbon-14 is exponentially decreasing function of the time.\r\n" );
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document.write( "According to the problem, the half-life is about 6000 years (5900 years, actually).\r\n" );
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document.write( "So we can write\r\n" );
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document.write( "    M(t) = .\r\n" );
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document.write( "We want to find \"t\", when M(t) = . So we write the decay equation in the form\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Our goal is to find \"t\" from this equation. \r\n" );
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document.write( "So, we divide both sides by , the initial mass of the Carbon-14, and we get\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Take logarithm base 10 from both sides\r\n" );
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document.write( "     = \r\n" );
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document.write( "    t =  = 9509.8 years, or 9500 years, rounded.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On radioactive Carbon-14 dating, see and learn from the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Using logarithms to solve real world problems \r
\n" ); document.write( "\n" ); document.write( "    - Radioactive decay problems \r
\n" ); document.write( "\n" ); document.write( "    - Carbon dating problems \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Logarithms\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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