document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143991>Question 143991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A model for the number of people N in a college community who have heard a rumor is given by the equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=P%281-e%5E%28-0.15d%29%29 ALIGN=MIDDLE  ALT=\"N=P%281-e%5E%28-0.15d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where P is the total population of the community and d is the number of days elapsed since the rumor began. If the number of students is 1,000 find the number of days when 500 students would have heard the rumor. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104804 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=104804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=P%281-e%5E%28-0.15d%29%29 ALIGN=MIDDLE  ALT=\"N=P%281-e%5E%28-0.15d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500=1000%281-e%5E%28-0.15d%29%29 ALIGN=MIDDLE  ALT=\"500=1000%281-e%5E%28-0.15d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=500 ALIGN=MIDDLE  ALT=\"N=500\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1000 ALIGN=MIDDLE  ALT=\"P=1000\"   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=500%2F1000=%281-e%5E%28-0.15d%29%29 ALIGN=MIDDLE  ALT=\"500%2F1000=%281-e%5E%28-0.15d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 1000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=1-e%5E%28-0.15d%29 ALIGN=MIDDLE  ALT=\"1%2F2=1-e%5E%28-0.15d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2-1=-e%5E%28-0.15d%29 ALIGN=MIDDLE  ALT=\"1%2F2-1=-e%5E%28-0.15d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2=-e%5E%28-0.15d%29 ALIGN=MIDDLE  ALT=\"-1%2F2=-e%5E%28-0.15d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F2%29%2F%28-1%29=e%5E%28-0.15d%29 ALIGN=MIDDLE  ALT=\"%28-1%2F2%29%2F%28-1%29=e%5E%28-0.15d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 (this will remove the negative sign from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-e ALIGN=MIDDLE  ALT=\"-e\"   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=1%2F2=e%5E%28-0.15d%29 ALIGN=MIDDLE  ALT=\"1%2F2=e%5E%28-0.15d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281%2F2%29=ln%28e%5E%28-0.15d%29%29 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=ln%28e%5E%28-0.15d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281%2F2%29=ln%28e%5E%28-0.15d%29%29 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=ln%28e%5E%28-0.15d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281%2F2%29=-0.15d%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=-0.15d%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the expression using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%5Ey%29=y%2Aln%28x%29%29 ALIGN=MIDDLE  ALT=\"ln%28x%5Ey%29=y%2Aln%28x%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%281%2F2%29=-0.15d%281%29 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=-0.15d%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of \"e\" to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281%2F2%29=-0.15d ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=-0.15d\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281%2F2%29%2F%28-0.15%29=d ALIGN=MIDDLE  ALT=\"ln%281%2F2%29%2F%28-0.15%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -0.15 to isolate d\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-ln%281%2F2%29%2F%280.15%29 ALIGN=MIDDLE  ALT=\"d=-ln%281%2F2%29%2F%280.15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=4.62098 ALIGN=MIDDLE  ALT=\"d=4.62098\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So in a little more than 4 and half days, 500 students will have heard the rumor\r<BR>\n" );
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