document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136373>Question 1136373</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A bacteria culture starts with 360 bacteria and grows at a rate proportional to its size. After 2 hours there will be 720 bacteria. \r<BR>\n" );
document.write( "\n" );
document.write( "(a) Express the population after t hours as a function of t. <BR>\n" );
document.write( "population: <BR>\n" );
document.write( " (function of t) \r<BR>\n" );
document.write( "\n" );
document.write( "(b) What will be the population after 9 hours? <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "(c) How long will it take for the population to reach 2810 ? <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 #754187 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P=Ab^t, t is hours and P is total and A is beginning<BR>\n" );
document.write( "720=360*b^2<BR>\n" );
document.write( "b^2=2<BR>\n" );
document.write( "b= sqrt (2)=1.414.  P=360* sqrt(2)^t\r<BR>\n" );
document.write( "\n" );
document.write( "After 9 hours  it would be 360*b^9=8134.81 or 8135.<BR>\n" );
document.write( "To reach 2880, this would be doubling three times so a little fewer than 6 hours to reach 2810<BR>\n" );
document.write( "Mathematically, 2810=360*sqrt(2)^n<BR>\n" );
document.write( "7.81=sqrt(2)^n<BR>\n" );
document.write( "ln both sides<BR>\n" );
document.write( "2.05=n *0.3466<BR>\n" );
document.write( "rounding at end 5.93 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );