document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196819>Question 196819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!\r<BR>\n" );
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document.write( "I've been having some trouble with the following word problem\r<BR>\n" );
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document.write( "A large pond is stocked with fish. The fish population P is modeled by the formula P = 4t + 8&#8730;t + 110, where t is the number of days since the fish were first introduced into the pond. How many days will it take for the fish population to reach 500?\r<BR>\n" );
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document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147549 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=147549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is the given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=4t%2Bsqrt%28t%2B110%29 ALIGN=MIDDLE  ALT=\"P=4t%2Bsqrt%28t%2B110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ???\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=4t%2Bsqrt%28t%2B110%29 ALIGN=MIDDLE  ALT=\"P=4t%2Bsqrt%28t%2B110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500=4t%2Bsqrt%28t%2B110%29 ALIGN=MIDDLE  ALT=\"500=4t%2Bsqrt%28t%2B110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=500 ALIGN=MIDDLE  ALT=\"P=500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500-4t=sqrt%28t%2B110%29 ALIGN=MIDDLE  ALT=\"500-4t=sqrt%28t%2B110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4t from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28500-4t%29%5E2=%28sqrt%28t%2B110%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28500-4t%29%5E2=%28sqrt%28t%2B110%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28500-4t%29%5E2=t%2B110 ALIGN=MIDDLE  ALT=\"%28500-4t%29%5E2=t%2B110\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square the square root to eliminate it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250000-4000t%2B16t%5E2=t%2B110 ALIGN=MIDDLE  ALT=\"250000-4000t%2B16t%5E2=t%2B110\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250000-4000t%2B16t%5E2-t-110=0 ALIGN=MIDDLE  ALT=\"250000-4000t%2B16t%5E2-t-110=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2-4001t%2B249890=0 ALIGN=MIDDLE  ALT=\"16t%5E2-4001t%2B249890=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At%5E2%2BBt%2BC ALIGN=MIDDLE  ALT=\"At%5E2%2BBt%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=16 ALIGN=MIDDLE  ALT=\"A=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-4001 ALIGN=MIDDLE  ALT=\"B=-4001\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=249890 ALIGN=MIDDLE  ALT=\"C=249890\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28-4001%29+%2B-+sqrt%28+%28-4001%29%5E2-4%2816%29%28249890%29+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=16 ALIGN=MIDDLE  ALT=\"A=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-4001 ALIGN=MIDDLE  ALT=\"B=-4001\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=249890 ALIGN=MIDDLE  ALT=\"C=249890\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%284001+%2B-+sqrt%28+%28-4001%29%5E2-4%2816%29%28249890%29+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%284001+%2B-+sqrt%28+%28-4001%29%5E2-4%2816%29%28249890%29+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4001 ALIGN=MIDDLE  ALT=\"-4001\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4001 ALIGN=MIDDLE  ALT=\"4001\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%284001+%2B-+sqrt%28+16008001-4%2816%29%28249890%29+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%284001+%2B-+sqrt%28+16008001-4%2816%29%28249890%29+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4001 ALIGN=MIDDLE  ALT=\"-4001\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16008001 ALIGN=MIDDLE  ALT=\"16008001\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%284001+%2B-+sqrt%28+16008001-15992960+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%284001+%2B-+sqrt%28+16008001-15992960+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2816%29%28249890%29 ALIGN=MIDDLE  ALT=\"4%2816%29%28249890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15992960 ALIGN=MIDDLE  ALT=\"15992960\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%284001+%2B-+sqrt%28+15041+%29%29%2F%282%2816%29%29 ALIGN=MIDDLE  ALT=\"t+=+%284001+%2B-+sqrt%28+15041+%29%29%2F%282%2816%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15992960 ALIGN=MIDDLE  ALT=\"15992960\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16008001 ALIGN=MIDDLE  ALT=\"16008001\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15041 ALIGN=MIDDLE  ALT=\"15041\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%284001+%2B-+sqrt%28+15041+%29%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%284001+%2B-+sqrt%28+15041+%29%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%284001+%2B-+13%2Asqrt%2889%29%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%284001+%2B-+13%2Asqrt%2889%29%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%284001%2B13%2Asqrt%2889%29%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%284001%2B13%2Asqrt%2889%29%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%284001-13%2Asqrt%2889%29%29%2F%2832%29 ALIGN=MIDDLE  ALT=\"t+=+%284001-13%2Asqrt%2889%29%29%2F%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=128.864 ALIGN=MIDDLE  ALT=\"t=128.864\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=121.199 ALIGN=MIDDLE  ALT=\"t=121.199\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use a calculator to approximate\r<BR>\n" );
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document.write( "Now because plugging in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=128.864 ALIGN=MIDDLE  ALT=\"t=128.864\"   DISABLED_style= \"max-width:90%; height:auto;\" > back in the second equation results in a contradiction, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=128.864 ALIGN=MIDDLE  ALT=\"t=128.864\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a solution.\r<BR>\n" );
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document.write( "So the only solution is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=121.199 ALIGN=MIDDLE  ALT=\"t=121.199\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that it will take about 122 days (rounding up to the nearest whole number) for the fish population to reach 500. </SPAN>\n" );
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