document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256916>Question 256916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of bacteria p in a pond after t hours is p(t). The more bacteria there are, the more rapidly the number increases. This is expressed by the equation p'(t)= 2p(t) . Find the most general exponential function of the form A*e^Kt which satisfies the equation. (A and K are constants. Hint: substitute this function into the equation and see what you get). \r<BR>\n" );
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document.write( "p(t)= \r<BR>\n" );
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document.write( "If there were 1500 bacteria at t=0, how many are there 2 hours later? \r<BR>\n" );
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document.write( "p(2)= <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 #188979 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=188979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dp%2Fdt=2p ALIGN=MIDDLE  ALT=\"dp%2Fdt=2p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dp%2Fp=2dt ALIGN=MIDDLE  ALT=\"dp%2Fp=2dt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Integrate,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28p%29=2t%2BC ALIGN=MIDDLE  ALT=\"ln%28p%29=2t%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=Ce%5E%282t%29 ALIGN=MIDDLE  ALT=\"p=Ce%5E%282t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When t=0, p=1500.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28t%29=1500e%5E%282t%29 ALIGN=MIDDLE  ALT=\"p%28t%29=1500e%5E%282t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At t=2 hours,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28t%29=1500e%5E%282%282%29%29=1500e%5E%284%29 ALIGN=MIDDLE  ALT=\"p%28t%29=1500e%5E%282%282%29%29=1500e%5E%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or approximately,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=81897 ALIGN=MIDDLE  ALT=\"p=81897\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );