document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048271>Question 1048271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve theproblem using the exponential model and population growth.\r<BR>\n" );
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document.write( "-A researcher is investigating a specimen of bacteria. She finds that the original 1000 bacteria grew to 2,048,000 in 60 hours. How fast does the bacteria (a) double? (b) quadruple? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #663877 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=663877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ce^kt=2048000<BR>\n" );
document.write( "t=60; C=1000<BR>\n" );
document.write( "1000*e^60k=2048000<BR>\n" );
document.write( "e^60k=2048=2^11, after dividing by 1000.  1024 is 2^10, and 2048 is 2^11.<BR>\n" );
document.write( "ln of both sides<BR>\n" );
document.write( "60k=11 ln2<BR>\n" );
document.write( "k=11ln2/60=0.1271<BR>\n" );
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document.write( "Cd=Ce^(0.1271)t<BR>\n" );
document.write( "divide by C, and Cd/C=2, since it is doubling.<BR>\n" );
document.write( "2=e^(0.1271)t<BR>\n" );
document.write( "ln of both sides<BR>\n" );
document.write( "ln2=0.1271 t; ln of e removes it<BR>\n" );
document.write( "0.693=0.1271t<BR>\n" );
document.write( "t=5.45 hours<BR>\n" );
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document.write( "quadruple<BR>\n" );
document.write( "ln 4=0.1271t<BR>\n" );
document.write( "t=ln4/0.127=10.90 hours, or recognize that doubling twice is quadrupling.<BR>\n" );
document.write( "from 1000 to 2048000 is 11 doubling times, and 60/11=5.45 </SPAN>\n" );
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