document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85209>Question 85209</A>: <I><SPAN STYLE=\"word-break: break-all;\">    In most businesses, increasing prices of products can negatively impact the number of customers. A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare.\r<BR>\n" );
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document.write( "   Let the number of riders be a function of the fare charged.  Graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), and find the slope of the graph.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61414 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=61414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let F = amount taken in per day in fares<BR>\n" );
document.write( "Let n = number of $.25 fare increases<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+%28800+-+40n%29%282.25+%2B+.25n%29 ALIGN=MIDDLE  ALT=\"F+=+%28800+-+40n%29%282.25+%2B+.25n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This equation just states<BR>\n" );
document.write( "Fares taken in = (number of riders)(fare far each rider)<BR>\n" );
document.write( "But the problem wants F as a function of the number of riders, so<BR>\n" );
document.write( "Let r = riders per day, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+800+-+40n ALIGN=MIDDLE  ALT=\"r+=+800+-+40n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40n+=+800+-+r ALIGN=MIDDLE  ALT=\"40n+=+800+-+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28800+-+r%29%2F40 ALIGN=MIDDLE  ALT=\"n+=+%28800+-+r%29%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+r%2A%28+2.25+%2B+%28800+-+r%29%2F160%29 ALIGN=MIDDLE  ALT=\"F+=+r%2A%28+2.25+%2B+%28800+-+r%29%2F160%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+2.25r+%2B+5r+-+r%5E2+%2F+160 ALIGN=MIDDLE  ALT=\"F+=+2.25r+%2B+5r+-+r%5E2+%2F+160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+-+r%5E2+%2F+160+%2B+7.25r ALIGN=MIDDLE  ALT=\"F+=+-+r%5E2+%2F+160+%2B+7.25r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By my calculations, when F is a maximum, n = 5.5, so the fare increase<BR>\n" );
document.write( "should be between $1.00 and $1.25. Then F = $2102.50 and r = 580<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-200%2C1500%2C+-200%2C2500%2C+-.00625x%5E2+%2B+7.25x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-200%2C1500%2C+-200%2C2500%2C+-.00625x%5E2+%2B+7.25x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );