document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161300>Question 1161300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a town is modelled by the function P=6t^2+110t+4000<BR>\n" );
document.write( "Where P is the population and t is the time in years since 2000.\r<BR>\n" );
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document.write( "a) What will the population be in 2020?\r<BR>\n" );
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document.write( "b) When will the population be 6000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784821 by </B><A HREF=/tutors/aboutme.mpl?userid=saw><B>saw(34)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=saw><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=784821\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solution.<BR>\n" );
document.write( "As the condition given<BR>\n" );
document.write( "t represents time in years<BR>\n" );
document.write( "P represents population<BR>\n" );
document.write( "(a)Time in 2020 = 2020-2000 = 20<BR>\n" );
document.write( "P = 6t^2+110t+4000<BR>\n" );
document.write( "P = 6(20)^2+(110*20)+4000<BR>\n" );
document.write( "Evaluate the power<BR>\n" );
document.write( "P= 6*400+(110*20)+4000<BR>\n" );
document.write( "Multiply the numbers<BR>\n" );
document.write( "P = 2400+2200+4000<BR>\n" );
document.write( "Add the numbers<BR>\n" );
document.write( "P = 8600<BR>\n" );
document.write( "Population will be 8600 in 2020.<BR>\n" );
document.write( "(b)When the population be 6000<BR>\n" );
document.write( "P = 6t^2+110t+4000<BR>\n" );
document.write( "Use substitution<BR>\n" );
document.write( "6000 = 6t^2+110t+4000<BR>\n" );
document.write( "Move expression to the left side and change its sign<BR>\n" );
document.write( "6000-6t^2-110t-4000 = 0<BR>\n" );
document.write( "Subtract the terms<BR>\n" );
document.write( "2000-6t^2-110t = 0<BR>\n" );
document.write( "Use the commutative property to reorder the terms<BR>\n" );
document.write( "-6t^2-110t+2000 = 0<BR>\n" );
document.write( "Divide both sides of the equation by -2<BR>\n" );
document.write( "3t^2+55t-1000 = 0<BR>\n" );
document.write( "Solve the quadratic equation<BR>\n" );
document.write( "ax^2+bx+c = 0 using<BR>\n" );
document.write( "x = (-b±√(b²-4ac))/2a<BR>\n" );
document.write( "t = (-55±√(55²-4*3*-1000))/2*3<BR>\n" );
document.write( "t = (-55±√15025)/6<BR>\n" );
document.write( "simplify the root<BR>\n" );
document.write( "t = (-55±5√601)/6<BR>\n" );
document.write( "Separate the solutions<BR>\n" );
document.write( "t₁ = (-55+5√601)/6<BR>\n" );
document.write( "t₂ = (-55-5√601)/6<BR>\n" );
document.write( "Alternative form<BR>\n" );
document.write( "t₁ = -29.59608<BR>\n" );
document.write( "t₂ = 11.26275<BR>\n" );
document.write( "Since negative value is not possible for the time in years<BR>\n" );
document.write( "t = 11.26275\r<BR>\n" );
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document.write( " </SPAN>\n" );
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