document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176270>Question 1176270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A	   bone	   is	   measured	   for	   its	   age	   and	   it	   is	   found	   that	   it	   contains	   87.5	   grams	   of	   Nitrogen-­‐14	   for	   every	   12.5	   grams	   of	   Carbon-­‐14;	   how	   old	   is	   the	   bone?	    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #802768 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=802768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to solve this question, you need to know the rate of decay in the carbon 14.<BR>\n" );
document.write( "when it decays, it turns into nitrogen.<BR>\n" );
document.write( "best i can think of with this information is that the total grams is 87.5 + 12.5 = 100 grams.\r<BR>\n" );
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document.write( "the carbon is only 12.5/100 = .125 of its original mass.\r<BR>\n" );
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document.write( "the half life of carbon is 5730 years.\r<BR>\n" );
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document.write( "the formula to use is f = p * .5 ^ n<BR>\n" );
document.write( "n is equal to 1 for every 5730 years.<BR>\n" );
document.write( "f is the ratio of carbon to mass in the future.<BR>\n" );
document.write( "p is the ratio of carbon to mass in the present.\r<BR>\n" );
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document.write( "when n = 1, the formula becomes f = 1 * .5 ^ 1 = .5<BR>\n" );
document.write( "to find the number of years, multiply n by 5730 to get 5730 years.\r<BR>\n" );
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document.write( "to solve for when f = .125, the formula becomes .125 = 1 * .5 ^ n<BR>\n" );
document.write( "simplify to get .125 = .5 ^ n<BR>\n" );
document.write( "take the log of both side of the equation to get:<BR>\n" );
document.write( "log(.125) = log(.5 ^ n)<BR>\n" );
document.write( "by the law of logs that says log(x^n) = n * log(x), the formula becomes:<BR>\n" );
document.write( "log(.125) = n * log(.5)<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = log(.125) / log(.5) = 3\r<BR>\n" );
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document.write( "since n represents 5730 years, then the age of the bone is estimated to be 3 * 5730 = 17190 years.\r<BR>\n" );
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document.write( "i tried to get a reference that specifically addresses the raltionship between carbon 14 and nitrogen 14 but was unsuccessful.\r<BR>\n" );
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document.write( "any answer more sophisticated than this required much further study in how bones are dated.\r<BR>\n" );
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document.write( "my assumptions are basic.\r<BR>\n" );
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document.write( "when the bone was alive, the mass was all carbon 14.<BR>\n" );
document.write( "as the bone dies, it loses carbon 14 which gets transformed to nitrogen.\r<BR>\n" );
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document.write( "not being a chemist, this is the best i can do.\r<BR>\n" );
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document.write( "from an algebraic standpoint it makes sense, but not knowing the ratio of carbon to nitrogen in a living organism, it's only a guess.\r<BR>\n" );
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document.write( "here's a reference that talks about the issue, but discusses carbon 12 as well.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.nde-ed.org/Physics/X-Ray/carbon14dating.xhtml\" target = \"_blank\">https://www.nde-ed.org/Physics/X-Ray/carbon14dating.xhtml</a>\r<BR>\n" );
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document.write( "an excerpt from that article is shown below.\r<BR>\n" );
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document.write( "How do scientist use Carbon-14 to determine the age of an artifact?\r<BR>\n" );
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document.write( "To measure the amount of radiocarbon left in a artifact, scientists burn a small piece to convert it into carbon dioxide gas. Radiation counters are used to detect the electrons given off by decaying Carbon-14 as it turns into nitrogen. In order to date the artifact, the amount of Carbon-14 is compared to the amount of Carbon-12 (the stable form of carbon) to determine how much radiocarbon has decayed. The ratio of carbon-12 to carbon-14 is the same in all living things. However, at the moment of death, the amount of carbon-14 begins to decrease because it is unstable, while the amount of carbon-12 remains constant in the sample. Half of the carbon-14 degrades every 5,730 years as indicated by its half-life. By measuring the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of the artifact.\r<BR>\n" );
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