document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192769>Question 1192769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A population of microorganisms grows according to the function p(x) = 100+0.2x+0.5x^2, where x is given in hours. How many hours does it take to reach population of 250 microorganisms? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824666 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A population of microorganisms grows according to the function p(x) = 100+0.2x+0.5x^2, <BR>\n" );
document.write( "where x is given in hours. How many hours does it take to reach population of 250 microorganisms?<BR>\n" );
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document.write( "To answer the question, you should solve this quadratic equation\r\n" );
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document.write( "    100 + 0.2x + 0.5x^2 = 250.\r\n" );
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document.write( "Reduce the equation to the standard form quadratic equation\r\n" );
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document.write( "    0.5x^2 + 0.2x - 150 = 0\r\n" );
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document.write( "and apply the quadratic formula.  You will get the roots\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -17.5217,   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 17.1217.\r\n" );
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document.write( "According to the meaning of the problem, you ignore the negative root and accept the positive one.\r\n" );
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document.write( "Your <U>ANSWER</U> is the value  x= 17.1217 hours.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "On solving quadratic equations using the quadratic formula, &nbsp;see the lessons \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/proof-of-quadratic-by-completing-the-square.lesson>PROOF of quadratic formula by completing the square</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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