document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179719>Question 1179719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 3 hours there will be 480 bacteria.\r<BR>\n" );
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document.write( "(a) Express the population P after t hours as a function of t.\r<BR>\n" );
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document.write( "P(t)= <BR>\n" );
document.write( "  <BR>\n" );
document.write( "(b) What will be the population after 4 hours?<BR>\n" );
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document.write( "(c) How long will it take for the population to reach 2770? Round your answer to two decimal places.<BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809384 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809384\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size.<BR>\n" );
document.write( " After 3 hours there will be 480 bacteria.<BR>\n" );
document.write( "(a) Express the population P after t hours as a function of t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29=+p%2A2%5E%28tk%29 ALIGN=MIDDLE  ALT=\"P%28t%29=+p%2A2%5E%28tk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where<BR>\n" );
document.write( "P(t) = 480<BR>\n" );
document.write( "p = 160<BR>\n" );
document.write( "t = 3<BR>\n" );
document.write( "k = constant<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160%2A2%5E%283k%29+=+480 ALIGN=MIDDLE  ALT=\"160%2A2%5E%283k%29+=+480\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%283k%29+=+480%2F160 ALIGN=MIDDLE  ALT=\"2%5E%283k%29+=+480%2F160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%283k%29+=+3 ALIGN=MIDDLE  ALT=\"2%5E%283k%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using logs<BR>\n" );
document.write( "3k*ln(2) = ln(3)<BR>\n" );
document.write( "3k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2830%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%2830%29%2Fln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3k = 1.585<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.585%2F3 ALIGN=MIDDLE  ALT=\"1.585%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k = .528<BR>\n" );
document.write( "The equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+p%2A2%5E%28.528t%29 ALIGN=MIDDLE  ALT=\"P%28t%29+=+p%2A2%5E%28.528t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "(b) What will be the population after 4 hours?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+160%2A2%5E%28.528%2A4%29 ALIGN=MIDDLE  ALT=\"P%28t%29+=+160%2A2%5E%28.528%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "p(t) = 692<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(c) How long will it take for the population to reach 2770?<BR>\n" );
document.write( " Round your answer to two decimal places.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160%2A2%5E%28.528t%29+=+2770 ALIGN=MIDDLE  ALT=\"160%2A2%5E%28.528t%29+=+2770\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28.528t%29+=+2770%2F160 ALIGN=MIDDLE  ALT=\"2%5E%28.528t%29+=+2770%2F160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28.528t%29+=+17.3125 ALIGN=MIDDLE  ALT=\"2%5E%28.528t%29+=+17.3125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".528t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2817.315%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%2817.315%29%2Fln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".528t = 4.1137<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.1137%2F.528 ALIGN=MIDDLE  ALT=\"4.1137%2F.528\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 7.79 hrs </SPAN>\n" );
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