document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38296>Question 38296</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Mesopatamian civilization was dated by using the carbon-14 dating. A piece of wood discovered in an archaeological dig was found to have lost 62% of its carbon-14. Determine its age.\r<BR>\n" );
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document.write( "The answer is 7997 years but I don't know how to get to that answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24664 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you need to know the halflife of C-14. It is 5730 years.\r<BR>\n" );
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document.write( "Formula for half-life, T is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+%28ln%282%29%29%2F%28y%29+ ALIGN=MIDDLE  ALT=\"+T+=+%28ln%282%29%29%2F%28y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where y is the \"time constant\".\r<BR>\n" );
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document.write( "We need to figure out the time constant first:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5730+=+%28ln%282%29%29%2Fy+ ALIGN=MIDDLE  ALT=\"+5730+=+%28ln%282%29%29%2Fy+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28ln%282%29%29%2F%285730%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28ln%282%29%29%2F%285730%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 0.000120968 years^(-1)\r<BR>\n" );
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document.write( "Right then: exponential decay has a generic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+N%5B0%5D%2Ae%5E%28-yt%29+ ALIGN=MIDDLE  ALT=\"+N+=+N%5B0%5D%2Ae%5E%28-yt%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "where N is the amount left \"now\" and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%5B0%5D+ ALIGN=MIDDLE  ALT=\"+N%5B0%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the original amount.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N%2FN%5B0%5D+=+e%5E%28-yt%29+ ALIGN=MIDDLE  ALT=\"+N%2FN%5B0%5D+=+e%5E%28-yt%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now, we are told that the carbon14 has reduced by 62%. So, if there was originally 100g of it, there now is 38g... a reduction of 62%. So, we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2838%2F100%29+=+e%5E%28-yt%29+ ALIGN=MIDDLE  ALT=\"+%2838%2F100%29+=+e%5E%28-yt%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.38+=+e%5E%28-yt%29+ ALIGN=MIDDLE  ALT=\"+0.38+=+e%5E%28-yt%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%280.38%29+=+-yt+ ALIGN=MIDDLE  ALT=\"+ln%280.38%29+=+-yt+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28ln%280.38%29%29%2F%28-y%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28ln%280.38%29%29%2F%28-y%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28ln%280.38%29%29%2F%28-0.000120968%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28ln%280.38%29%29%2F%28-0.000120968%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Working this out gives you 7998.7 years, which is in agreement with your answer, assuming rounding errors and the value of the half life used by the question.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
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