document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153986>Question 1153986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The table lists a readings for three years. <BR>\n" );
document.write( "​(a) If the quadratic relationship between the carbon dioxide concentration C and the year t is expressed as Upper C equals at squared plus bt plus c​, where t equals 0 corresponds to​ 1962, use a system of linear equations to determine the constants​ a, b, and​ c, and give the equation.<BR>\n" );
document.write( "​(b) Predict the year when the amount of carbon dioxide in the atmosphere will double from its 1962 level.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Year.      <BR>\n" );
document.write( "1962<BR>\n" );
document.write( "1982<BR>\n" );
document.write( "2002\r<BR>\n" );
document.write( "\n" );
document.write( "CO2<BR>\n" );
document.write( "319<BR>\n" );
document.write( "340<BR>\n" );
document.write( "368<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776334 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=776334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+at%5E2%2Bbt%2Bc ALIGN=MIDDLE  ALT=\"C+=+at%5E2%2Bbt%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where t=0 corresponds to 1962.<br><BR>\n" );
document.write( "data:<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "   year   t     C\r\n" );
document.write( "  ----------------\r\n" );
document.write( "   1962   0    319\r\n" );
document.write( "   1982  20    340\r\n" );
document.write( "   2002  40    368<br></PRE><BR>\n" );
document.write( "(a) determine the coefficients a, b, and c and write the equation<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Equations:<br>\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+319 ALIGN=MIDDLE  ALT=\"c+=+319\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1]\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400a%2B20b%2Bc+=+340 ALIGN=MIDDLE  ALT=\"400a%2B20b%2Bc+=+340\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600a%2B40b%2Bc+=+368 ALIGN=MIDDLE  ALT=\"1600a%2B40b%2Bc+=+368\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [3]<br>\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400a%2B20b+=+21 ALIGN=MIDDLE  ALT=\"400a%2B20b+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [4] (from [1] and [2])\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1600a%2B40b+=+49 ALIGN=MIDDLE  ALT=\"1600a%2B40b+=+49\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [5] (from [1] and [3]<br>\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800a%2B40b+=+42 ALIGN=MIDDLE  ALT=\"800a%2B40b+=+42\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [6] ([4], doubled)<br>\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800a+=+7 ALIGN=MIDDLE  ALT=\"800a+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ([5]-[6])\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+7%2F800 ALIGN=MIDDLE  ALT=\"a+=+7%2F800\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [7]<br>\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2B40b+=+49 ALIGN=MIDDLE  ALT=\"14%2B40b+=+49\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (from [5] and [7])\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40b+=+35 ALIGN=MIDDLE  ALT=\"40b+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+7%2F8 ALIGN=MIDDLE  ALT=\"b+=+7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br></PRE><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "a = 7/800<BR>\n" );
document.write( "b =7/8<BR>\n" );
document.write( "c = 319<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+%287%2F800%29t%5E2%2B%287%2F8%29t%2B319 ALIGN=MIDDLE  ALT=\"C+=+%287%2F800%29t%5E2%2B%287%2F8%29t%2B319\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(b) Find the year when C = 2(319) = 638<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F800%29t%5E2%2B%287%2F8%29t%2B319+=+638 ALIGN=MIDDLE  ALT=\"%287%2F800%29t%5E2%2B%287%2F8%29t%2B319+=+638\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solving algebraically is certainly possible, but very tedious.<br><BR>\n" );
document.write( "Graph the function and the constant 638 on a graphing calculator and find where they intersect.<br><BR>\n" );
document.write( "A graph:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-50%2C200%2C-100%2C800%2C%287%2F800%29x%5E2%2B%287%2F8%29x%2B319%2C638%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The intersection of the two graphs, to the nearest whole number, is 147, indicating the year 1962+147 = 2109.<br><BR>\n" );
document.write( "ANSWER: year 2109<br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );