document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32568>Question 32568</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of deer living in an enclosed game reserve displays regular fluctuations in size.  Wildlife biologists have chosen to model the population size with a sinusoidal function.  At its height the deer population is 7000, while at its low it is 2000.  The time between highs and lows is 6 months.  The population at the start of January, 2001 is 4500 and decreasing.  Consider January, 2001 to correspond to time t = 0.\r<BR>\n" );
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document.write( "a)	Model the deer population as a function of time t in months.  \r<BR>\n" );
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document.write( "I'm just having a little trouble with the actual function for this one, I managed to figure out the graph I think but can't figure out how to set up the function with the numbers given. Please help if you can...\r<BR>\n" );
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document.write( "Thanks a bunch, you guys are always such a big help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19037 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=19037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equation you want is y=Asin(BX+C)+D<BR>\n" );
document.write( "amplitude = A = (7000-2000)/2=2500<BR>\n" );
document.write( "period = 6 mths = (2pi/B); so B=pi/6<BR>\n" );
document.write( "Shift = -C/B=-C/[pi/6]; shift is 6 mths to the left; <BR>\n" );
document.write( "So -C/[pi/6]=+6 and C=-pi<BR>\n" );
document.write( "Translation is +4500; so D=4500<BR>\n" );
document.write( "Equation is y=2500sin[(pi/6)t-pi]+4500<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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