document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1060946>Question 1060946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The logistic growth function f(t) = ((( 400 / 1+9.0e-0.22t ))) describes the population of a species of butterflies tmonths after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months?\r<BR>\n" );
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document.write( "    a. 480 butterflies<BR>\n" );
document.write( "    b. 401 butterflies<BR>\n" );
document.write( "    c. 244 butterflies<BR>\n" );
document.write( "    d. 4800 butterflies </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675802 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=675802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What you meant is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > months after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > butterflies  are introduced, the  habitat will contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29=400%2F%281%2B9%2Ae%5E%28-0.22t%29%29 ALIGN=MIDDLE  ALT=\"f%28t%29=400%2F%281%2B9%2Ae%5E%28-0.22t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > butterflies.<BR>\n" );
document.write( "That tells you that for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=40 ALIGN=MIDDLE  ALT=\"f%280%29=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29 ALIGN=MIDDLE  ALT=\"f%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > , but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29%3C400 ALIGN=MIDDLE  ALT=\"f%28t%29%3C400\"   DISABLED_style= \"max-width:90%; height:auto;\" > at all times.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12 ALIGN=MIDDLE  ALT=\"t=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the approximate calculation (rounding to whole numbers) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2812%29=400%2F%281%2B9%2Ae%5E%28-0.22%2A12%29%29=400%2F%281%2B9%2Ae%5E%28-2.46%29%29=400%2F%281%2B9%2A0.071361%29=400%2F%281%2B0.64225%29=400%2F1.64225=244 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE: Since the problem is multiple choice, with only one choice below 400,<BR>\n" );
document.write( "and the function tells you that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29%3C400 ALIGN=MIDDLE  ALT=\"f%28t%29%3C400\"   DISABLED_style= \"max-width:90%; height:auto;\" > at all times,<BR>\n" );
document.write( "the only choice was c) 244 butteries.<BR>\n" );
document.write( "No calculation was needed in this case. </SPAN>\n" );
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