document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866914>Question 866914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of bacteria N in a culture is modeled by\r<BR>\n" );
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document.write( "    N = 100 ekt\r<BR>\n" );
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document.write( "where t is the time in hours. If N=150 when t=3, what is the time (in hours) required for the original population to double in size ?<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 #522601 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</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=522601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> NOT this, <i>N = 100 ekt,</i><BR>\n" );
document.write( "but THIS:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=100e%5E%28kt%29 ALIGN=MIDDLE  ALT=\"N=100e%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You want to first find what is k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28N%29=ln%28100%29%2Bkt%2A1 ALIGN=MIDDLE  ALT=\"ln%28N%29=ln%28100%29%2Bkt%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kt=ln%28N%29-ln%28100%29 ALIGN=MIDDLE  ALT=\"kt=ln%28N%29-ln%28100%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_green%28k=%281%2Ft%29ln%28N%2F100%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=%281%2Ft%29ln%28N%2F100%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting the given data from the description,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F3%29ln%28150%2F100%29 ALIGN=MIDDLE  ALT=\"k=%281%2F3%29ln%28150%2F100%29\"   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%2F3%29ln%281.5%29 ALIGN=MIDDLE  ALT=\"k=%281%2F3%29ln%281.5%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_green%28k=0.135%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=0.135%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you have the model as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28N=100e%5E%280.135t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28N=100e%5E%280.135t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Remember this:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kt=ln%28N%29-ln%28100%29 ALIGN=MIDDLE  ALT=\"kt=ln%28N%29-ln%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, since you want to know t for when N=200, solve for t, ...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%281%2F0.135%29%28ln%28200%2F100%29%29 ALIGN=MIDDLE  ALT=\"t=%281%2F0.135%29%28ln%28200%2F100%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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