document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042169>Question 1042169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Contagious disease enters a college campus, and the number of students infected by the disease is given by n=15000/(1+999e^(-0.8x)) where x is the number of days after the disease appears on a campus. \r<BR>\n" );
document.write( "\n" );
document.write( "a.) How many students had the disease when it appeared on campus?<BR>\n" );
document.write( "b.) What is the upper limit of the number of students infected by the disease? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657113 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=657113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "a) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The initial count n happens when x = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug in x = 0 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15000%2F%281%2B999e%5E%28-0.8x%29%29 ALIGN=MIDDLE  ALT=\"n=15000%2F%281%2B999e%5E%28-0.8x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15000%2F%281%2B999e%5E%28-0.8%2A0%29%29 ALIGN=MIDDLE  ALT=\"n=15000%2F%281%2B999e%5E%28-0.8%2A0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15000%2F%281%2B999e%5E%280%29%29 ALIGN=MIDDLE  ALT=\"n=15000%2F%281%2B999e%5E%280%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15000%2F%281%2B999%2A1%29 ALIGN=MIDDLE  ALT=\"n=15000%2F%281%2B999%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15000%2F%281%2B999%29 ALIGN=MIDDLE  ALT=\"n=15000%2F%281%2B999%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15000%2F%281000%29 ALIGN=MIDDLE  ALT=\"n=15000%2F%281000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15 ALIGN=MIDDLE  ALT=\"n=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So 15 students had the disease when it appeared on campus. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice how as x gets larger and larger, the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=999e%5E%28-0.8x%29 ALIGN=MIDDLE  ALT=\"999e%5E%28-0.8x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gets smaller.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Using limits, as x approaches infinity,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=999e%5E%28-0.8x%29 ALIGN=MIDDLE  ALT=\"999e%5E%28-0.8x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > approaches 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So effectively <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15000%2F%281%2B999e%5E%28-0.8x%29%29 ALIGN=MIDDLE  ALT=\"n=15000%2F%281%2B999e%5E%28-0.8x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > turns into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15000%2F%281%2B0%29 ALIGN=MIDDLE  ALT=\"n=15000%2F%281%2B0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > when x gets very very large. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+15000 ALIGN=MIDDLE  ALT=\"n+=+15000\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the limiting value. This is the upper ceiling so to speak of all the number of people who can get infected. The value of n won't actually reach 15000 but it will get closer and closer. <BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );