document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24646>Question 24646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At noon, there were 1000 bacteria in a culture dish.  The formula for the growth of the bacteria is n = l000(2a), where n is the number of bacteria, and a is the number of hours the culture has been growing.  How many bacteria will there be at 18:00, assuming none of the culture die?  a is an exponent.\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "(k2lm2)(-kn)2  ..the 2's are exponents.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13130 by </B><A HREF=/tutors/aboutme.mpl?userid=quentin252><B>quentin252(19)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=quentin252><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=13130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> okay, so n=1000*(2^a)<BR>\n" );
document.write( "and at 18:00 hrs a=6   (since 18:00=6pm is 6 hrs past noon=12:00)<BR>\n" );
document.write( "so n=1000*(2^6)=1000*64=64000 at 18:00 hrs.\r<BR>\n" );
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document.write( "next,<BR>\n" );
document.write( "as above I'll represent exponents with ^ symbol<BR>\n" );
document.write( "k^2*l*m^2*(-kn)^2<BR>\n" );
document.write( "order of operations<BR>\n" );
document.write( "1. parenthesis: well nothing to do here, \"-kn\" is reduced<BR>\n" );
document.write( "2. next exponents<BR>\n" );
document.write( "   so the k is squared = k^2<BR>\n" );
document.write( "      the m (not the lm) is squared = m^2<BR>\n" );
document.write( "  and the -kn is squared --   <BR>\n" );
document.write( "  (-kn)^2=(-k)^2 * n^2 = k^2 * n^2<BR>\n" );
document.write( "3. so now comes the products (left to right)<BR>\n" );
document.write( "   giving us k^2 * l * m^2 * k^2 * n^2<BR>\n" );
document.write( "   grouping the k's gives us : k^4 * l * m^2 * n^2<BR>\n" );
document.write( "   or in spiffy notation : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E4%2Al%2Am%5E2%2An%5E2 ALIGN=MIDDLE  ALT=\"k%5E4%2Al%2Am%5E2%2An%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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