document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129948>Question 1129948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The spread of a flu virus in a community of 45,000 people is given by the function<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+%2845000%29%2F%281%2B224e%5E%28-899t%29%29 ALIGN=MIDDLE  ALT=\"f%28t%29+=+%2845000%29%2F%281%2B224e%5E%28-899t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where f(t) is the number do people infected in week t.<BR>\n" );
document.write( "a.) How many people had the flu at the outbreak of the epidemic?<BR>\n" );
document.write( "b.) When will half the twin be infected?<BR>\n" );
document.write( "(Remember to show all work and give exact answers) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746566 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=746566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+%2845000%29%2F%281%2B224e%5E%28-0.899t%29%29 ALIGN=MIDDLE  ALT=\"f%28t%29+=+%2845000%29%2F%281%2B224e%5E%28-0.899t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "NOTE: The exponential e^(-899t) indicates an outbreak that affects all 45000 people in the community in a matter of hours or perhaps minutes, instead of weeks.  I will assume for my answer that the exponential is supposed to be e^(-0.899t).<br><BR>\n" );
document.write( "(a) At the outbreak of the epidemic, t (the number of weeks after the outbreak) is 0, so evaluate f(0):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29+=+%2845000%29%2F%281%2B224e%5E%28-0.899%280%29%29%29+=+45000%2F%281%2B224%281%29%29+=+45000%2F225+=+200 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 200 people had the flu at the outbreak.<br><BR>\n" );
document.write( "(b) Half the population is 22500, so we want to find t when f(t)=22500.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22500+=+%2845000%29%2F%281%2B224e%5E%28-0.899t%29%29 ALIGN=MIDDLE  ALT=\"22500+=+%2845000%29%2F%281%2B224e%5E%28-0.899t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B224e%5E%28-0.899t%29+=+45000%2F22500+=+2 ALIGN=MIDDLE  ALT=\"1%2B224e%5E%28-0.899t%29+=+45000%2F22500+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=224e%5E%28-0.899t%29+=+1 ALIGN=MIDDLE  ALT=\"224e%5E%28-0.899t%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-0.899t%29+=+1%2F224 ALIGN=MIDDLE  ALT=\"e%5E%28-0.899t%29+=+1%2F224\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.899t+=+ln%281%2F224%29 ALIGN=MIDDLE  ALT=\"-0.899t+=+ln%281%2F224%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28ln%281%2F224%29%29%2F-0.899 ALIGN=MIDDLE  ALT=\"t+=+%28ln%281%2F224%29%29%2F-0.899\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "which to 5 decimal places is 6.01963<br><BR>\n" );
document.write( "ANSWER: Half the town will be infected after a little more than 6 weeks. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );