document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=64439>Question 64439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two parter that I don't understand.  Can anyone help me? \r<BR>\n" );
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document.write( "The black bear population in a certain are in Alaska is approximated by \r<BR>\n" );
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document.write( "B(t) = 580/1 + 8.3e^-0.12t, \r<BR>\n" );
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document.write( "t is the number of years after logging ended in the area.  How many black bearsare there 5 years after logging ended?  Predict how long it will take for the black bear population to reach 290.  \r<BR>\n" );
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document.write( "Thanks again. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45090 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=45090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The black bear population in a certain are in Alaska is approximated by <BR>\n" );
document.write( "B(t) = 580/1 + 8.3e^-0.12t, <BR>\n" );
document.write( "t is the number of years after logging ended in the area. How many black bears are there 5 years after logging ended? Predict how long it will take for the black bear population to reach 290.<BR>\n" );
document.write( "Comment: Your formula is ambiguous.  It is difficult to tell where<BR>\n" );
document.write( "the denominator starts and where it ends.  I'm going to assume 1+8.3e^-0.12t<BR>\n" );
document.write( "is all in the denominator.<BR>\n" );
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document.write( "B(t) = 580/[1 + 8.3e^-0.12t]<BR>\n" );
document.write( "B(5)=580/[1+8.3e^(-0.12*5)<BR>\n" );
document.write( "B(5)=580/5.55513658<BR>\n" );
document.write( "B(5)=104.4 bears<BR>\n" );
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document.write( "If B(t)=290 find \"t\".<BR>\n" );
document.write( "290=580/(1+8.3e^(-0.12t)<BR>\n" );
document.write( "1+8.3e^(-0.12t)=580/290=2<BR>\n" );
document.write( "8.3e^(-0.12t)=1<BR>\n" );
document.write( "e^(-0.12t)=0.1204819277...<BR>\n" );
document.write( "Take the natural log of both sides to get:<BR>\n" );
document.write( "-0.12t=-2.11625555...<BR>\n" );
document.write( "t=17.635 years<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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