document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115542>Question 1115542</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An accident in 1986 at the Chernobyl nuclear plant in Ukraine released a large amount of plutonium (Pu-239) into the atmosphere. The half-life of Pu-239 is about 24,110 years. Find the decay constant. Use the function N(t)=Noe^-kt to find what remains of an initial 20 grams of Pu-239 after 5000 years. How long will it take for these 20 grams to decay to 1 gram? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #730399 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=730399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> N(t)=Noe^-kt\r<BR>\n" );
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document.write( "Do it this way in pure text<BR>\n" );
document.write( "N(t)=N[o]e^(-kt)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29=N%5Bo%5De%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"N%28t%29=N%5Bo%5De%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Reassigning variables for typewriting convenience:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=ne%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"N=ne%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, N for function and n for initial quantity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28N%29=ln%28ne%5E%28-kt%29%29 ALIGN=MIDDLE  ALT=\"ln%28N%29=ln%28ne%5E%28-kt%29%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=ln%28N%29=ln%28n%29%2B%28-kt%29%2A1 ALIGN=MIDDLE  ALT=\"ln%28N%29=ln%28n%29%2B%28-kt%29%2A1\"   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=-kt%2Bln%28n%29=ln%28N%29 ALIGN=MIDDLE  ALT=\"-kt%2Bln%28n%29=ln%28N%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=-kt=ln%28N%29-ln%28n%29 ALIGN=MIDDLE  ALT=\"-kt=ln%28N%29-ln%28n%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=kt=ln%28n%29-ln%28N%29 ALIGN=MIDDLE  ALT=\"kt=ln%28n%29-ln%28N%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=k=%28ln%28n%29-ln%28N%29%29%2Ft ALIGN=MIDDLE  ALT=\"k=%28ln%28n%29-ln%28N%29%29%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You were given half-life is 24110 years.  This means  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28n%2FN%29=ln%281%2F%281%2F2%29%29=ln%282%29 ALIGN=MIDDLE  ALT=\"ln%28n%2FN%29=ln%281%2F%281%2F2%29%29=ln%282%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=highlight%28k=ln%282%29%2Ft%29 ALIGN=MIDDLE  ALT=\"highlight%28k=ln%282%29%2Ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%282%29%2F24110 ALIGN=MIDDLE  ALT=\"k=ln%282%29%2F24110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=0.00002875%29 ALIGN=MIDDLE  ALT=\"highlight%28k=0.00002875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The original model,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28highlight%28N%28t%29=N%5Bo%5De%5E%28-0.00002875t%29%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28highlight%28N%28t%29=N%5Bo%5De%5E%28-0.00002875t%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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