document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102688>Question 1102688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The formula  P=0.67x2–0.042x + 1 models the approximate population (P), in thousands, for a species of fish in a local pond, x years after 1997.  During what year will the population reach 54,892 fish?\r<BR>\n" );
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document.write( "I got about 2090 using the quadratic equation. However, the fact that I had to round to get a whole answer makes me think I got it wrong. Is it correct?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717427 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor overlooked the fact that the formula gives the number of fish in thousands, not the actual number of fish.  Otherwise his method is a perfectly good way to get the answer.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.67x%5E2-0.042x%2B1+=+54.892 ALIGN=MIDDLE  ALT=\"0.67x%5E2-0.042x%2B1+=+54.892\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For a quadratic equation with \"ugly\" coefficients like this, it's by far easiest to use a graphing calculator or some other tool to find the solution.  I used my TI83 to graph the function and the constant to see where they intersect:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-2%2C12%2C-15%2C85%2C0.67x%5E2-0.042x%2B1%2C54.892%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-2%2C12%2C-15%2C85%2C0.67x%5E2-0.042x%2B1%2C54.892%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This is clearly a contrived problem, as the solution turns out to be exactly 9.<br><BR>\n" );
document.write( "Since x is the number of years after 1997, the answer is 2006. </SPAN>\n" );
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