document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192217>Question 192217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of new cars purchased in a city can be modeled by the equation C =18t^2 + 174t + 6241, where C is the number of new cars and t = 0 corresponds to the number of new cars purchased in 1972.  In what year will the number of new cars reach 35,000?  I have tried using the quadratic equation, but I get a strange answer.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144264 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=144264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "I presume you performed the calculation thusly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ C(t) = 18t^2 + 174t + 6241\">\r<BR>\n" );
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document.write( "Where\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ C(t) = 35000\">\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 18t^2 + 174t + 6241 = 35000\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 18t^2 + 174t -28759 = 0\">\r<BR>\n" );
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document.write( "Using the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t = \frac{-174 \pm sqrt{174^2 - 4(18)(-28579)}}{2(18)} \">\r<BR>\n" );
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document.write( "Which, after a bit of prime factoring work and calculator button punching becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t = \frac{-29 \pm 7\sqrt{397}}{6} \approx 35.4\">\r<BR>\n" );
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document.write( "Now, reading the problem carefully, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE C(0) = 6241\"> is the number of new cars sold in 1972.  That means that 6241 new cars were sold by the <i><b>end of</b></i> 1972.  So, 35 years later, you would be at the end of 1972 plus 35 = 2007, and at that time you would not have quite reached the 35,000 number. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE C(35) = 18(35)^2 + 174(35) + 6241 = 34381\">.  So you trip the 35,000 number right around 3:22 AM June 5, 2008, roughly speaking.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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