document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252075>Question 252075</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bacteria culture grows by the exponential model y = 200ekt. How many bacteria<BR>\n" );
document.write( "are there initially? If the number of bacteria triples in 2 hours, find the number of<BR>\n" );
document.write( "bacteria after 5 hours. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183818 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=183818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> All exponential models are of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Y+=+Ae%5Ekt ALIGN=MIDDLE  ALT=\"+Y+=+Ae%5Ekt\"   DISABLED_style= \"max-width:90%; height:auto;\" > where A is \"initial value\", k is \"growth rate\", t is time units, and Y is \"ending value\".\r<BR>\n" );
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document.write( "So, initially there were 200 bacteria. Since we triple, Y = 3*200 = 600. Now for time; t = 2. We don't know the growth rate, k. This is step 1 in these kind of problems.\r<BR>\n" );
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document.write( "Our formula now becomes first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+600+=+200e%5E%282k%29 ALIGN=MIDDLE  ALT=\"+600+=+200e%5E%282k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+e%5E2k ALIGN=MIDDLE  ALT=\"3+=+e%5E2k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and taking a natural log (LN) of both sides we get ln(3) = 2k, and finally solving for k, we get k = ln(3)/2.\r<BR>\n" );
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document.write( "Knowing k, we can now find how many there are after 5 hours.\r<BR>\n" );
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document.write( "Y = 200*e^(5*ln(3)/2) becomes Y = 3118 rounded to the nearest bacteria. </SPAN>\n" );
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