document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006197>Question 1006197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a city with a population of 70,000 people, the number of people P(t) exposed to a rumor in t hours is given by the function <BR>\n" );
document.write( "P(t) = 70,000(1 &#8722; e^&#8722;0.0009t).(Round your answers to the nearest hour.)\r<BR>\n" );
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document.write( "(a) Find the number of hours until 10% of the population have heard the rumor.\r<BR>\n" );
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document.write( "(b) Find the number of hours until 90% of the population have heard the rumor. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622352 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=622352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%28t%29+=+70000%2A%28+1+-+e%5E%28-.0009t%29+%29+ ALIGN=MIDDLE  ALT=\"+P%28t%29+=+70000%2A%28+1+-+e%5E%28-.0009t%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "When is the ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%28t%29+%2F+70000+=+.1+ ALIGN=MIDDLE  ALT=\"+P%28t%29+%2F+70000+=+.1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%28t%29+=+.1%2A70000+ ALIGN=MIDDLE  ALT=\"+P%28t%29+=+.1%2A70000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%28t%29+=+7000+ ALIGN=MIDDLE  ALT=\"+P%28t%29+=+7000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7000+=+70000%2A%28+1+-+e%5E%28-.0009t%29+%29+ ALIGN=MIDDLE  ALT=\"+7000+=+70000%2A%28+1+-+e%5E%28-.0009t%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=+.1+=+1+-+e%5E%28+-.0009t+%29+ ALIGN=MIDDLE  ALT=\"+.1+=+1+-+e%5E%28+-.0009t+%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+-.0009t+%29+=+.9+ ALIGN=MIDDLE  ALT=\"+e%5E%28+-.0009t+%29+=+.9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the natural log of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.0009t+=+ln%28.9%29+ ALIGN=MIDDLE  ALT=\"+-.0009t+=+ln%28.9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.0009t+=+-.10536+ ALIGN=MIDDLE  ALT=\"+-.0009t+=+-.10536+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+117.07+ ALIGN=MIDDLE  ALT=\"+t+=+117.07+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In 117.07 hrs, 10% have heard rumor<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Follow the same steps:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.9+=+1+-+e%5E%28+-.0009t+%29+ ALIGN=MIDDLE  ALT=\"+.9+=+1+-+e%5E%28+-.0009t+%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+-.0009t+%29+=+.1+ ALIGN=MIDDLE  ALT=\"+e%5E%28+-.0009t+%29+=+.1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.0009t+=+ln%28.1%29+ ALIGN=MIDDLE  ALT=\"+-.0009t+=+ln%28.1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.0009t+=+-2.3026+ ALIGN=MIDDLE  ALT=\"+-.0009t+=+-2.3026+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+2558.43+ ALIGN=MIDDLE  ALT=\"+t+=+2558.43+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In 2558.43 hrs, 90% have heard rumor<BR>\n" );
document.write( "-------------------------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );