document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202641>Question 202641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain bacterial infection has 110,000 organisms at 12:00pm. At 12:30 pm the population was 140,000. If this growth rate has been steady, when did the infection start? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152830 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=152830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A certain bacterial infection has 110,000 organisms at 12:00pm. At 12:30 pm the population was 140,000. If this growth rate has been steady, when did the infection start?<BR>\n" );
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document.write( "A(t) = Ao*(r)^t<BR>\n" );
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document.write( "r is the rate of growth<BR>\n" );
document.write( "t is the time in minutes<BR>\n" );
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document.write( "140,000 = 110,000*r^(30)<BR>\n" );
document.write( "14/11 = r^(30)<BR>\n" );
document.write( "Take the log:<BR>\n" );
document.write( "30*log(r) = log(14/11)<BR>\n" );
document.write( "log(r) = [log(14/11)]/30<BR>\n" );
document.write( "log(r) = 0.0034911784<BR>\n" );
document.write( "r = 10^0.0034911784<BR>\n" );
document.write( "r = 1.008071133 per minute<BR>\n" );
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document.write( "1 = 110,000(1.008071133)^t<BR>\n" );
document.write( "1.008071133)^t = 110,000^-1<BR>\n" );
document.write( "t*log(1.998071133) = -log(110,000)<BR>\n" );
document.write( "t = -16.7705 minutes<BR>\n" );
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document.write( "12:00 - 16.77 minutes is approximately 11:43 am<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );