document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171737>Question 1171737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Initially, 10 students at Kampung Tembikai contracted influenza. The flu spread<BR>\n" );
document.write( "over time and the total number of students who eventually contracted the flu<BR>\n" );
document.write( "approached but never exceeded 200. Let P(𝑡) denote the number of students who<BR>\n" );
document.write( "had contracted the flu after 𝑡 days, where P is an appropriate function.<BR>\n" );
document.write( "Sketch the graph of P and indicate where the function is increasing by showing the<BR>\n" );
document.write( "interval. If the horizontal asymptote exists, what would the line be? Discuss the<BR>\n" );
document.write( "concavity of the graph by explaining its significance. Identify the inflection point and<BR>\n" );
document.write( "explain why it exist. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796676 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(t)=L/(1+Be^-(kt))<BR>\n" );
document.write( "when t=0, P(t)=10<BR>\n" );
document.write( "The denominator is 1+B, and L/(1+B)=10<BR>\n" );
document.write( "L=10+10B<BR>\n" );
document.write( "-<BR>\n" );
document.write( "L=200, the horizontal asymptote.  When k is large, Be^-(kt) becomes close to 0 and the denominator 1.<BR>\n" );
document.write( "Since L=10+10B, B=19<BR>\n" );
document.write( "P(t)=200/(1+19 e^(-kt))<BR>\n" );
document.write( "The inflection point is where the 2nd derivative goes from positive to negative and is at L/2 or 100 cases.<BR>\n" );
document.write( "The horizontal asymptote is at P(t)=200. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C40%2C-10%2C200%2C200%2F%281%2B19e%5E%28-0.25x%29%29%2C100%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C40%2C-10%2C200%2C200%2F%281%2B19e%5E%28-0.25x%29%29%2C100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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