document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=397720>Question 397720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rare species of insect was discovered in the Amazon Rain Forest. In order to protect the species, environmentalists declare the insect endangered and transplant the insect to a protected area. The population of the insect (t) months after being translated is given by P: P(t)= 50(1+0.5t)/(2+0.01t)\r<BR>\n" );
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document.write( "A. How many insects were discovered? In other words, what was the population when t=0?<BR>\n" );
document.write( "B. What will the population be after 5 years?<BR>\n" );
document.write( "C. Determine the horizontal asymptote of P(t). What is the largest population the protected area can sustain? Explain why. (Hint: use the calculator to help you. Choose a good window.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281805 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=281805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+50%281%2B.5t%29%2F%282%2B.01t%29+=+%2850+%2B+25t%29%2F%282+%2B+.01t%29 ALIGN=MIDDLE  ALT=\"P%28t%29+=+50%281%2B.5t%29%2F%282%2B.01t%29+=+%2850+%2B+25t%29%2F%282+%2B+.01t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A: Just replace t = 0 to obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%29+=+25 ALIGN=MIDDLE  ALT=\"P%280%29+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "B: Replace t with 60 (since 60 months equals 5 years)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2860%29+=+%2850+%2B+25%2860%29%29%2F%282+%2B+.01%2860%29%29+=+596.1538 ALIGN=MIDDLE  ALT=\"P%2860%29+=+%2850+%2B+25%2860%29%29%2F%282+%2B+.01%2860%29%29+=+596.1538\"   DISABLED_style= \"max-width:90%; height:auto;\" > (round to 596)\r<BR>\n" );
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document.write( "C: A horizontal asymptote occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3Einfinity%2C+%2850+%2B+25t%29%2F%282+%2B+.01t%29%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3Einfinity%2C+%2850+%2B+25t%29%2F%282+%2B+.01t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a finite number. In this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3Einfinity%2C+%2850+%2B+25t%29%2F%282+%2B+.01t%29%29+=+25%2F.01+=+2500 ALIGN=MIDDLE  ALT=\"lim%28x-%3Einfinity%2C+%2850+%2B+25t%29%2F%282+%2B+.01t%29%29+=+25%2F.01+=+2500\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so 2500 is the maximum attainable population. </SPAN>\n" );
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