document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=387822>Question 387822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A biologist finds that the population of a certain type of bacteria doubles each half-hour. An initial culture has 90 bacteria.<BR>\n" );
document.write( "How long will it take for the number of bacteria to reach 368,640? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274168 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=274168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A biologist finds that the population of a certain type of bacteria doubles each half-hour. An initial culture has 90 bacteria.<BR>\n" );
document.write( "How long will it take for the number of bacteria to reach 368,640?<BR>\n" );
document.write( "------<BR>\n" );
document.write( "A(t) = Ao*2^(2t)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "368640 = 90*2^(2t)<BR>\n" );
document.write( "4096 = 2^(2t)<BR>\n" );
document.write( "(2t)ln(2) = ln(4096)<BR>\n" );
document.write( "2t = ln(4096)/ln(2)<BR>\n" );
document.write( "2t = 12<BR>\n" );
document.write( "t = 6 hours<BR>\n" );
document.write( "============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============ </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );