document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194023>Question 194023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The fish population of a lake is modeled by the function \r<BR>\n" );
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document.write( "P=(10)/(1+4e^(-0.8t))\r<BR>\n" );
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document.write( "where, P is the number of fish in thousands and t is the  years since the lake was stocked.\r<BR>\n" );
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document.write( "What is the fish population (correct up to two decimal places) after 3 years is? [Remember: If P=3.15, then there are 3,150 fish)\r<BR>\n" );
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document.write( "How many years will it take for the fish population to reach 7,000? (correct up to two decimal places) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145647 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=145647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  P is the number of fish in thousands<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3 ALIGN=MIDDLE  ALT=\"t+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=10+%2F+%281+%2B+4e%5E%28-.8t%29%29 ALIGN=MIDDLE  ALT=\"P=10+%2F+%281+%2B+4e%5E%28-.8t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=10+%2F+%281+%2B+4e%5E%28-2.4%29%29 ALIGN=MIDDLE  ALT=\"P=10+%2F+%281+%2B+4e%5E%28-2.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=10+%2F+%281+%2B+4%2A.0907%29 ALIGN=MIDDLE  ALT=\"P=10+%2F+%281+%2B+4%2A.0907%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=10+%2F+%281+%2B+.3629%29 ALIGN=MIDDLE  ALT=\"P=10+%2F+%281+%2B+.3629%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=10+%2F+%281.3629%29 ALIGN=MIDDLE  ALT=\"P=10+%2F+%281.3629%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+7.34 ALIGN=MIDDLE  ALT=\"P+=+7.34\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the population is 7,340 after 3 years<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+7 ALIGN=MIDDLE  ALT=\"P+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=10+%2F+%281%2B4e%5E%28-.8t%29%29 ALIGN=MIDDLE  ALT=\"P=10+%2F+%281%2B4e%5E%28-.8t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=10+%2F+%281%2B4e%5E%28-.8t%29%29 ALIGN=MIDDLE  ALT=\"7=10+%2F+%281%2B4e%5E%28-.8t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B4e%5E%28-.8t%29%29 ALIGN=MIDDLE  ALT=\"%281%2B4e%5E%28-.8t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A%281%2B4e%5E%28-.8t%29%29+=+10 ALIGN=MIDDLE  ALT=\"7%2A%281%2B4e%5E%28-.8t%29%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+4e%5E%28-.8t%29+=+10%2F7 ALIGN=MIDDLE  ALT=\"1+%2B+4e%5E%28-.8t%29+=+10%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4e%5E%28-.8t%29+=+3%2F7 ALIGN=MIDDLE  ALT=\"4e%5E%28-.8t%29+=+3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-.8t%29+=+3%2F28 ALIGN=MIDDLE  ALT=\"e%5E%28-.8t%29+=+3%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the ln of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.8t+=+ln%28.10714%29 ALIGN=MIDDLE  ALT=\"-.8t+=+ln%28.10714%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.8t+=+-2.2336 ALIGN=MIDDLE  ALT=\"-.8t+=+-2.2336\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2.79 ALIGN=MIDDLE  ALT=\"t+=+2.79\"   DISABLED_style= \"max-width:90%; height:auto;\" > years </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );