document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102611>Question 102611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The doubling time for e-coli= 20 minutes<BR>\n" );
document.write( "Mass of the e-coli bacterium =10 to the -12g<BR>\n" );
document.write( "Mass of the earth =5.9763* 10 to the 24kg\r<BR>\n" );
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document.write( "•	What is the mass of a colony of e coli after 1 day (24hrs) of exponential growth from one single e-coli bacterium?\r<BR>\n" );
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document.write( "•	How long would it take to reach a mass equivalent to planet earth? \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 #75052 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=75052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Doubling time = 20 minutes\r<BR>\n" );
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document.write( "Mass of e. coli = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x10%5E-12 ALIGN=MIDDLE  ALT=\"1x10%5E-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >g\r<BR>\n" );
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document.write( "Mass of earth = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.9763x10%5E24 ALIGN=MIDDLE  ALT=\"5.9763x10%5E24\"   DISABLED_style= \"max-width:90%; height:auto;\" >kg<BR>\n" );
document.write( "For exponential growth problems, we need to determine the growth constant, k, which is related to the doubling time, T, by the following equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%282%29%2FT ALIGN=MIDDLE  ALT=\"k=ln%282%29%2FT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%282%29%2F20 ALIGN=MIDDLE  ALT=\"k=ln%282%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3.47x10%5E-2 ALIGN=MIDDLE  ALT=\"k=3.47x10%5E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The general form of an exponential equation is<BR>\n" );
document.write( "1. Find m at t=24 hours=1440 minutes, since doubling time is given in minutes for consistency. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kt=%283.47x10%5E-2%29%281440%29 ALIGN=MIDDLE  ALT=\"kt=%283.47x10%5E-2%29%281440%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kt=49.968 ALIGN=MIDDLE  ALT=\"kt=49.968\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+m%5B0%5D%2Ae%5E%2849.906%29 ALIGN=MIDDLE  ALT=\"m+=+m%5B0%5D%2Ae%5E%2849.906%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+1x10%5E-12%2Ae%5E%2849.906%29 ALIGN=MIDDLE  ALT=\"m+=+1x10%5E-12%2Ae%5E%2849.906%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+1x10%5E-12%2A4.72237x10%5E21 ALIGN=MIDDLE  ALT=\"m+=+1x10%5E-12%2A4.72237x10%5E21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+4.72x10%5E9 ALIGN=MIDDLE  ALT=\"m+=+4.72x10%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sice we're have mass and are looking for time, let's re-arrange the equation. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28m%29-ln%28m%5B0%5D%29=kt ALIGN=MIDDLE  ALT=\"ln%28m%29-ln%28m%5B0%5D%29=kt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28ln%28m%29-ln%28m%5B0%5D%29%29%2Fk ALIGN=MIDDLE  ALT=\"t=%28ln%28m%29-ln%28m%5B0%5D%29%29%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note 1 kg = 1000 g, the mass of the earth was converted to grams to keep units consistent. <BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28ln%285.9763x10%5E27%29-ln%281x10%5E-12%29%29%2F%283.47x10%5E-2%29 ALIGN=MIDDLE  ALT=\"t=%28ln%285.9763x10%5E27%29-ln%281x10%5E-12%29%29%2F%283.47x10%5E-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t=2639 minutes<BR>\n" );
document.write( "Thank goodness for that anti-bacterial soap.  </SPAN>\n" );
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