document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980288>Question 980288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 1995, 500 runners entered a marathon. In 1998, 20500 runners entered the race. Because of the limited number of facilities, the carrying capacity of the number of racers is 58500. The number of racers at any time, t, in years, can be modeled by the logistic function of p(t)=c/1+Be^kt\r<BR>\n" );
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document.write( "1. what is the value of c?<BR>\n" );
document.write( "2. what is the value of b?<BR>\n" );
document.write( "3. what is the value of k?\r<BR>\n" );
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document.write( "i know how to find the value of c and b but i need help on finding the value of K please, any help would be appreciated.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601449 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=601449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You should find that c = 58500 and b = 116.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28t%29+=+c%2F%281%2BBe%5E%28k%2At%29%29 ALIGN=MIDDLE  ALT=\"p%28t%29+=+c%2F%281%2BBe%5E%28k%2At%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=p%28t%29+=+58500%2F%281%2B116e%5E%28k%2At%29%29 ALIGN=MIDDLE  ALT=\"p%28t%29+=+58500%2F%281%2B116e%5E%28k%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in c = 58500 and b = 116\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20500+=+58500%2F%281%2B116e%5E%28k%2A3%29%29 ALIGN=MIDDLE  ALT=\"20500+=+58500%2F%281%2B116e%5E%28k%2A3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in t = 3 and p(t) = 20500 (since 3 years after 1995, the amount of runners is 20500)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20500%281%2B116e%5E%28k%2A3%29%29+=+58500 ALIGN=MIDDLE  ALT=\"20500%281%2B116e%5E%28k%2A3%29%29+=+58500\"   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=20500%2B2378000e%5E%283k%29+=+58500 ALIGN=MIDDLE  ALT=\"20500%2B2378000e%5E%283k%29+=+58500\"   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=2378000e%5E%283k%29+=+58500-20500 ALIGN=MIDDLE  ALT=\"2378000e%5E%283k%29+=+58500-20500\"   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=2378000e%5E%283k%29+=+38000 ALIGN=MIDDLE  ALT=\"2378000e%5E%283k%29+=+38000\"   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=e%5E%283k%29+=+38000%2F2378000 ALIGN=MIDDLE  ALT=\"e%5E%283k%29+=+38000%2F2378000\"   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=e%5E%283k%29+=+0.01597981497057 ALIGN=MIDDLE  ALT=\"e%5E%283k%29+=+0.01597981497057\"   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=3k+=+ln%280.01597981497057%29 ALIGN=MIDDLE  ALT=\"3k+=+ln%280.01597981497057%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=3k+=+-4.1364289175233 ALIGN=MIDDLE  ALT=\"3k+=+-4.1364289175233\"   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+=+-4.1364289175233%2F3 ALIGN=MIDDLE  ALT=\"k+=+-4.1364289175233%2F3\"   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+=+-1.37880963917443 ALIGN=MIDDLE  ALT=\"k+=+-1.37880963917443\"   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+=+-1.3788 ALIGN=MIDDLE  ALT=\"k+=+-1.3788\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounding to 4 decimal places)\r<BR>\n" );
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document.write( "So the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28t%29+=+58500%2F%281%2B116e%5E%28-1.3788t%29%29 ALIGN=MIDDLE  ALT=\"p%28t%29+=+58500%2F%281%2B116e%5E%28-1.3788t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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