document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=593293>Question 593293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Under ideal conditions, a population of rabbits has an exponential growth rate of 11.7% per day.  Consider an initial population of 200 rabbits.  Find the exponential growth function.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376284 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=376284\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The exponential growth function is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+N%5B0%5D%2Ae%5E%28kt%29 ALIGN=MIDDLE  ALT=\"N%28t%29+=+N%5B0%5D%2Ae%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where N(t) is the population at time t, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5B0%5D ALIGN=MIDDLE  ALT=\"N%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the initial population and k is the growth constant (some positive number in the interval [0,1])\r<BR>\n" );
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document.write( "In this case, the initial population is 200, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5B0%5D=200 ALIGN=MIDDLE  ALT=\"N%5B0%5D=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+N%5B0%5D%2Ae%5E%28kt%29 ALIGN=MIDDLE  ALT=\"N%28t%29+=+N%5B0%5D%2Ae%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29+=+200%2Ae%5E%28kt%29 ALIGN=MIDDLE  ALT=\"N%28t%29+=+200%2Ae%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The growth rate is 11.7% per day, so when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the population is now 200 + 0.117*200 = 223.4\r<BR>\n" );
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document.write( "So this means we have the equation \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=223.4+=+200%2Ae%5E%28k%29 ALIGN=MIDDLE  ALT=\"223.4+=+200%2Ae%5E%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's solve for k\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=223.4+=+200%2Ae%5E%28k%29 ALIGN=MIDDLE  ALT=\"223.4+=+200%2Ae%5E%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=223.4%2F200+=+e%5E%28k%29 ALIGN=MIDDLE  ALT=\"223.4%2F200+=+e%5E%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.117+=+e%5E%28k%29 ALIGN=MIDDLE  ALT=\"1.117+=+e%5E%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.117%29+=+ln%28e%5E%28k%29%29 ALIGN=MIDDLE  ALT=\"ln%281.117%29+=+ln%28e%5E%28k%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.117%29+=+k%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%281.117%29+=+k%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.117%29+=+k%2A%281%29 ALIGN=MIDDLE  ALT=\"ln%281.117%29+=+k%2A%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281.117%29+=+k ALIGN=MIDDLE  ALT=\"ln%281.117%29+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.110646520087064+=+k ALIGN=MIDDLE  ALT=\"0.110646520087064+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+0.110646520087064 ALIGN=MIDDLE  ALT=\"k+=+0.110646520087064\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the growth constant is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+0.110647 ALIGN=MIDDLE  ALT=\"k+=+0.110647\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the exponential growth function is \r<BR>\n" );
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