document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=327777>Question 327777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=Ie%5Ekt ALIGN=MIDDLE  ALT=\"N=Ie%5Ekt\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where N is the number of items in terms of the initial population I, at time t, and k is the growth constant equal to the percent of growth per unit of time. An artifact is discovered at a certain site. If it has 65% of the carbon-14 it originally contained, what is the approximzte age of the artifact?  (carbon-14 decays at the rate of 0.0125% annually.)\r<BR>\n" );
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document.write( "possible answers(5200 years, 3446 years, 1497 years, 2800 years.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #234758 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=234758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=Ie%5E%28kt%29 ALIGN=MIDDLE  ALT=\"N=Ie%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where N is the number of items in terms of the initial population <BR>\n" );
document.write( "I, at time t, and k is the growth constant equal to the percent of growth per unit of time. <BR>\n" );
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document.write( "An artifact is discovered at a certain site.<BR>\n" );
document.write( " If it has 65% of the carbon-14 it originally contained, what is the <BR>\n" );
document.write( "approximate age of the artifact?<BR>\n" );
document.write( " (carbon-14 decays at the rate of 0.0125% annually.)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ie%5E%28kt%29=N ALIGN=MIDDLE  ALT=\"Ie%5E%28kt%29=N\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where:<BR>\n" );
document.write( "N = .65<BR>\n" );
document.write( "I = 1<BR>\n" );
document.write( "k = -.000125, decay is negative <BR>\n" );
document.write( "Find t<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ae%5E%28-.000125t%29=+.65 ALIGN=MIDDLE  ALT=\"1%2Ae%5E%28-.000125t%29=+.65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using nat logs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%28-.000125t%29%29=+ln%28.65%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%28-.000125t%29%29=+ln%28.65%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find ln<BR>\n" );
document.write( "-.000125t = -.43078<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-.43078%29%2F%28-.000125%29 ALIGN=MIDDLE  ALT=\"%28-.43078%29%2F%28-.000125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = +3,446 yrs<BR>\n" );
document.write( " </SPAN>\n" );
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