document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1021925>Question 1021925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Really need help with this question, please show detailed workings and many thanks.\r<BR>\n" );
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document.write( "At an annual company dinner, the CEO announced that the company will be expanding its operations into other regions in South America and are looking for employees willing to travel around the region. There were two hundred employees who attended the company dinner. Two hours later, 350 employees had heard of this new opportunity. The number of employees who learned of the new program t hours later is given by the function:<BR>\n" );
document.write( "f(t)= 2500/(1+Be^(-kt))\r<BR>\n" );
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document.write( "1) Name the type of function given in the question.<BR>\n" );
document.write( "2) Find the value of B and k.<BR>\n" );
document.write( "3) Estimate the number of employees in the company. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #637633 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=637633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The function is exponential<BR>\n" );
document.write( "If I plot <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28t%29+ ALIGN=MIDDLE  ALT=\"+f%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the vertical axis<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the horizontal axis,<BR>\n" );
document.write( "then the points given are:<BR>\n" );
document.write( "( 0, 200 )<BR>\n" );
document.write( "( 2, 350 )<BR>\n" );
document.write( "Where the form is:<BR>\n" );
document.write( "( t, f(t) )<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28t%29+=+2500+%2F+%28+1+%2B+B%2Ae%5E%28+-kt+%29+%29+ ALIGN=MIDDLE  ALT=\"+f%28t%29+=+2500+%2F+%28+1+%2B+B%2Ae%5E%28+-kt+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug in the 1st point:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+200+=+2500+%2F+%28+1+%2B+B%2Ae%5E%28+-k%2A0+%29+%29+ ALIGN=MIDDLE  ALT=\"+200+=+2500+%2F+%28+1+%2B+B%2Ae%5E%28+-k%2A0+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+200+=+2500+%2F+%28+1+%2B+B+%29+ ALIGN=MIDDLE  ALT=\"+200+=+2500+%2F+%28+1+%2B+B+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28-k%2A0+%29+=+1+ ALIGN=MIDDLE  ALT=\"+e%5E%28-k%2A0+%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "Plug in the 2nd point:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+2500+%2F+%28+1+%2B+B%2Ae%5E%28+-k%2A2+%29+%29+ ALIGN=MIDDLE  ALT=\"+350+=+2500+%2F+%28+1+%2B+B%2Ae%5E%28+-k%2A2+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+200+=+2500+%2F+%28+1+%2B+B+%29+ ALIGN=MIDDLE  ALT=\"+200+=+2500+%2F+%28+1+%2B+B+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+%2B+B+=+2500+%2F+200+ ALIGN=MIDDLE  ALT=\"+1+%2B+B+=+2500+%2F+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B+=+12.5+-+1+ ALIGN=MIDDLE  ALT=\"+B+=+12.5+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B+=+11.5+ ALIGN=MIDDLE  ALT=\"+B+=+11.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this result into (2)<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+2500+%2F+%28+1+%2B+11.5%2Ae%5E%28+-k%2A2+%29+%29+ ALIGN=MIDDLE  ALT=\"+350+=+2500+%2F+%28+1+%2B+11.5%2Ae%5E%28+-k%2A2+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+%2B+11.5%2Ae%5E%28+-k%2A2+%29+=+2500+%2F+350+ ALIGN=MIDDLE  ALT=\"+1+%2B+11.5%2Ae%5E%28+-k%2A2+%29+=+2500+%2F+350+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+%2B+11.5%2Ae%5E%28+-k%2A2+%29+=+7.1429+ ALIGN=MIDDLE  ALT=\"+1+%2B+11.5%2Ae%5E%28+-k%2A2+%29+=+7.1429+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+11.5%2Ae%5E%28+-k%2A2+%29+=+6.1429+ ALIGN=MIDDLE  ALT=\"+11.5%2Ae%5E%28+-k%2A2+%29+=+6.1429+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28-2k+%29+=+.5342+ ALIGN=MIDDLE  ALT=\"+e%5E%28-2k+%29+=+.5342+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the natural log of both sides<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2k+=+ln%28+.5342+%29+ ALIGN=MIDDLE  ALT=\"+-2k+=+ln%28+.5342+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2k+=+-.627+ ALIGN=MIDDLE  ALT=\"+-2k+=+-.627+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+.3135+ ALIGN=MIDDLE  ALT=\"+k+=+.3135+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B+=+11.5+ ALIGN=MIDDLE  ALT=\"+B+=+11.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+.3135+ ALIGN=MIDDLE  ALT=\"+k+=+.3135+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "The number of employees woud be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28t%29+ ALIGN=MIDDLE  ALT=\"+f%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > approaches infinity<BR>\n" );
document.write( "( a very long time after company made announcement )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28t%29+=+2500+%2F+%28+1+%2B+B%2Ae%5E%28+-kt+%29+%29+ ALIGN=MIDDLE  ALT=\"+f%28t%29+=+2500+%2F+%28+1+%2B+B%2Ae%5E%28+-kt+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28-kt+%29+ ALIGN=MIDDLE  ALT=\"+e%5E%28-kt+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > approaches zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28t%29++=+2500+ ALIGN=MIDDLE  ALT=\"+f%28t%29++=+2500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The number of employees in company is 2500<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Check one of the given points:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+2500+%2F+%28+1+%2B+11.5%2Ae%5E%28+-k%2A2+%29+%29+ ALIGN=MIDDLE  ALT=\"+350+=+2500+%2F+%28+1+%2B+11.5%2Ae%5E%28+-k%2A2+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+2500+%2F+%28+1+%2B+11.5%2Ae%5E%28+-.3135%2A2+%29+%29+ ALIGN=MIDDLE  ALT=\"+350+=+2500+%2F+%28+1+%2B+11.5%2Ae%5E%28+-.3135%2A2+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+2500+%2F+%28+1+%2B+11.5%2Ae%5E%28+-.627+%29+%29+ ALIGN=MIDDLE  ALT=\"+350+=+2500+%2F+%28+1+%2B+11.5%2Ae%5E%28+-.627+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+2500+%2F+%28+1+%2B+11.5%2A.5342+%29+ ALIGN=MIDDLE  ALT=\"+350+=+2500+%2F+%28+1+%2B+11.5%2A.5342+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+2500+%2F+%28+1+%2B+6.1432+%29+ ALIGN=MIDDLE  ALT=\"+350+=+2500+%2F+%28+1+%2B+6.1432+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350+=+2500+%2F+7.1432+ ALIGN=MIDDLE  ALT=\"+350+=+2500+%2F+7.1432+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+350%2A7.1432+=+2500+ ALIGN=MIDDLE  ALT=\"+350%2A7.1432+=+2500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2500.12+=+2500+ ALIGN=MIDDLE  ALT=\"+2500.12+=+2500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Error due to rounding off, I think<BR>\n" );
document.write( "Hop I got it -tough problem! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );