document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978605>Question 978605</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain bacteria population is known to doubles every 90 minutes. Suppose that there are initially 160 bacteria. \r<BR>\n" );
document.write( "\n" );
document.write( "What is the size of the population after  t  hours?\r<BR>\n" );
document.write( "\n" );
document.write( "please help, ive sent this a few times and still have no response and or a legit answer. I've tried multiple times and im unsure what to do with the 90... so i convert that to hours? in the exponent?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599976 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=599976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P=Po{1+r}^1.5  ;;time is in hours. You could use minutes, but hours is what is desired and it makes the exponent smaller.\r<BR>\n" );
document.write( "\n" );
document.write( "P/Po=2 (doubling); Po=160<BR>\n" );
document.write( "2=(1+r)^1.5<BR>\n" );
document.write( "ln2 =1.5 * ln (1+r)\r<BR>\n" );
document.write( "\n" );
document.write( "0.693=1.5 *ln (1+r); divide by 1.5 both sides<BR>\n" );
document.write( "0.462=ln (1+r); raise both to e power\r<BR>\n" );
document.write( "\n" );
document.write( "1.5872=(1+r)<BR>\n" );
document.write( "r=0.5872\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "After t hours, the population, P=160 (1.5872)^t\r<BR>\n" );
document.write( "\n" );
document.write( "Check.  After 3 hours, the population has doubled twice or increased 4 times.\r<BR>\n" );
document.write( "\n" );
document.write( "P=160 (1+r)^3=160(1.5872)^3\r<BR>\n" );
document.write( "\n" );
document.write( "1.5872^3= 3.998, or 4 by rounding.<BR>\n" );
document.write( "P=160*4=640.  That is quadrupling.\r<BR>\n" );
document.write( "\n" );
document.write( "After 24 hours, the population has increased by 1440/90 or 16 doubling times or by a factor of 2^16<BR>\n" );
document.write( "2^16=65536\r<BR>\n" );
document.write( "\n" );
document.write( "P=160(1+ 0.5872)^24<BR>\n" );
document.write( "1.5872^24=65537, which is by rounding, very close to 65536, and that is 2^16<BR>\n" );
document.write( "P=160*65536=10,485,760<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );