document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=752776>Question 752776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> really need help and the step by step<BR>\n" );
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document.write( "In a colony of bacteria growing in a nutrient solution, the number of bacteria grows exponentially, and it doubles every 30 minutes. If the number of bacteria is initially 100,000. how many minutes will it take for the number of bacteria to reach 1,000,000  Round answer to nearest tenth of a minute. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458032 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=458032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Continuous exponential growth <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=p%2Ae%5E%28kt%29 ALIGN=MIDDLE  ALT=\"A=p%2Ae%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where A is amount at time t and p is the initial amount for t=0.\r<BR>\n" );
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document.write( "Doubles every 30 minutes ---- let us use time units in minutes.  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2p=p%2Ae%5E%28k%2A30%29 ALIGN=MIDDLE  ALT=\"2p=p%2Ae%5E%28k%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we want to have a value found for k.\r<BR>\n" );
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document.write( "Divide both sides by p.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=e%5E%28k%2A30%29 ALIGN=MIDDLE  ALT=\"2=e%5E%28k%2A30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29=30k%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%282%29=30k%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%282%29=30k ALIGN=MIDDLE  ALT=\"ln%282%29=30k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F30%29%2Aln%282%29 ALIGN=MIDDLE  ALT=\"k=%281%2F30%29%2Aln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=0.023%29 ALIGN=MIDDLE  ALT=\"highlight%28k=0.023%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The growth model for this example is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=p%2Ae%5E%280.023t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28A=p%2Ae%5E%280.023t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "t is time in minutes<BR>\n" );
document.write( "p is initial population for t=0<BR>\n" );
document.write( "A is population at some time t </SPAN>\n" );
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