document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314890>Question 314890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> this word problem uses a formula that the book talked about very briefly and I did not understand it...N=Iekt,where n = number of items in terms of the initial population, I, at time t, and k is the growth constant equal to the % of growth per unit of time\r<BR>\n" );
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document.write( "an artifact is found at a certain site.  If it has 65% of the carbon-14 it originally contained, what is the approximate age of the artifact?<BR>\n" );
document.write( "(carbon-14 decays at the rate of 0.0125% annually)<BR>\n" );
document.write( "please show work so I can understand this formula better and how to do the problem.\r<BR>\n" );
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document.write( "THANKS IN ADVANCE </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225280 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=225280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Your given equation:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "is the standard exponential growth/decay formula<BR>\n" );
document.write( "where<BR>\n" );
document.write( "N is the amount after time t<BR>\n" );
document.write( "I is the initial amount<BR>\n" );
document.write( "k is the growth/decay rate<BR>\n" );
document.write( "t is time<BR>\n" );
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document.write( "If k is positive it is \"growth\" otherwise k is negative or \"decay\".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Given your problem:<BR>\n" );
document.write( "an artifact is found at a certain site. If it has 65% of the carbon-14 it originally contained, what is the approximate age of the artifact?<BR>\n" );
document.write( "(carbon-14 decays at the rate of 0.0125% annually)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice the problem doesn't give you the initial amount so assign it a variable:<BR>\n" );
document.write( "Let x = initial amount<BR>\n" );
document.write( "then<BR>\n" );
document.write( "N is .65x<BR>\n" );
document.write( "I is x<BR>\n" );
document.write( "k is 0.0125% or 0.000125<BR>\n" );
document.write( "t is what we need to find<BR>\n" );
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document.write( "Plug in what was given into:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.65x+=+xe%5E%280.000125t%29 ALIGN=MIDDLE  ALT=\"+.65x+=+xe%5E%280.000125t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, solve for t:<BR>\n" );
document.write( "Start, by dividing both sides by x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.65+=+e%5E%280.000125t%29 ALIGN=MIDDLE  ALT=\"+.65+=+e%5E%280.000125t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next, take the natural log of both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28.65%29+=+0.000125t+ ALIGN=MIDDLE  ALT=\"+ln%28.65%29+=+0.000125t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28.65%29%2F0.000125+=+t+ ALIGN=MIDDLE  ALT=\"+ln%28.65%29%2F0.000125+=+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3446.26+=+t+ ALIGN=MIDDLE  ALT=\"+-3446.26+=+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > years<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Or, it is about 3446 years old.<BR>\n" );
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