document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032942>Question 1032942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a village can be modelled by the function P(x)= -22.5x^2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be the highest?\r<BR>\n" );
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document.write( "Much appreciated </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647549 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
document.write( "P(x) = -22.5x^2 + 428x + 1100<BR>\n" );
document.write( "To find maximum, differentiate:<BR>\n" );
document.write( "P'(x) = -45x + 428<BR>\n" );
document.write( "P'(x) = 0<BR>\n" );
document.write( "-45x + 428 = 0<BR>\n" );
document.write( "-45x = -428<BR>\n" );
document.write( "x = -428/-45<BR>\n" );
document.write( "x = 9.51<BR>\n" );
document.write( "Nature Table:<BR>\n" );
document.write( "......................... -     9.51    +<BR>\n" );
document.write( "-45x + 428....... +      0      -<BR>\n" );
document.write( "............................ /     -       \<BR>\n" );
document.write( "Maximum.<BR>\n" );
document.write( "Therefore after 9.5 years the population<BR>\n" );
document.write( "will be at its maximum.   <BR>\n" );
document.write( "-22.5(9.5) + 428(9.5) + 1100<BR>\n" );
document.write( "= 4952.<BR>\n" );
document.write( "Hope this helps :-) </SPAN>\n" );
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