document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088726>Question 1088726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The&#8203; half-life of&#8203; carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 73&#8203;% of the&#8203; carbon-14 expected in living&#8203; matter, when did the tree&#8203; die? \r<BR>\n" );
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document.write( "The tree died about ______ years ago?<BR>\n" );
document.write( "&#8203;(Do not round until the final answer. Then round to the nearest whole&#8203; number.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703074 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=703074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+P%2Ae%5E%28kt%29 ALIGN=MIDDLE  ALT=\"F+=+P%2Ae%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" > = future amount<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" > = present amount<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+ ALIGN=MIDDLE  ALT=\"k+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= constant of proportion.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time\r<BR>\n" );
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document.write( "half life of carbon is given by the equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5+=+e%5E%285600k%29 ALIGN=MIDDLE  ALT=\".5+=+e%5E%285600k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because:\r<BR>\n" );
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document.write( "half life of carbon is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5600 ALIGN=MIDDLE  ALT=\"5600\"   DISABLED_style= \"max-width:90%; height:auto;\" > years.\r<BR>\n" );
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document.write( "solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then you can solve the problem.\r<BR>\n" );
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document.write( "take log of both sides of equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5+=+e%5E%285600k%29 ALIGN=MIDDLE  ALT=\".5+=+e%5E%285600k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28.5%29+=+log%28e%5E%285600k%29%29 ALIGN=MIDDLE  ALT=\"log%28.5%29+=+log%28e%5E%285600k%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28.5%29+=+5600k+%2A+log%28e%29 ALIGN=MIDDLE  ALT=\"log%28.5%29+=+5600k+%2A+log%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "divide both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5600%2Alog%28e%29 ALIGN=MIDDLE  ALT=\"5600%2Alog%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+log%28.5%29%2F%285600%2Alog%28e%29%29 ALIGN=MIDDLE  ALT=\"k+=+log%28.5%29%2F%285600%2Alog%28e%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+ ALIGN=MIDDLE  ALT=\"k+\"   DISABLED_style= \"max-width:90%; height:auto;\" >to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-.301029996+%2F+%285600%2A.434294482%29 ALIGN=MIDDLE  ALT=\"k+=+-.301029996+%2F+%285600%2A.434294482%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-.000123776+ ALIGN=MIDDLE  ALT=\"k+=+-.000123776+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if the tree has only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=73 ALIGN=MIDDLE  ALT=\"73\"   DISABLED_style= \"max-width:90%; height:auto;\" >%=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.73 ALIGN=MIDDLE  ALT=\"0.73\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the carbon left, then your equation of: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+P+%2A+e%5E%28kt%29 ALIGN=MIDDLE  ALT=\"F+=+P+%2A+e%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.73+=+1%2Ae%5E%28k%2At%29 ALIGN=MIDDLE  ALT=\".73+=+1%2Ae%5E%28k%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.73+=+e%5E%28-.000123776%2At%29 ALIGN=MIDDLE  ALT=\".73+=+e%5E%28-.000123776%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28.73%29+=+log%28e%5E%28-.000123776%2At%29%29 ALIGN=MIDDLE  ALT=\"log%28.73%29+=+log%28e%5E%28-.000123776%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28.73%29+=+-.000123776%2At%2Alog%28e%29 ALIGN=MIDDLE  ALT=\"log%28.73%29+=+-.000123776%2At%2Alog%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "divide both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.000123776%2Alog%28e%29 ALIGN=MIDDLE  ALT=\"-.000123776%2Alog%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+log%28.73%29+%2F+%28-.000123776%2Alog%28e%29%29 ALIGN=MIDDLE  ALT=\"t+=+log%28.73%29+%2F+%28-.000123776%2Alog%28e%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2542.58 ALIGN=MIDDLE  ALT=\"t+=+2542.58\"   DISABLED_style= \"max-width:90%; height:auto;\" > years\r<BR>\n" );
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document.write( "Then round to the nearest whole number:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2543 ALIGN=MIDDLE  ALT=\"t+=+2543\"   DISABLED_style= \"max-width:90%; height:auto;\" > years\r<BR>\n" );
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document.write( " </SPAN>\n" );
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