document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=800472>Question 800472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SAT scores One small college has observed a downward trend in the average SAT score of applicants to the college. Analysis has resulted to the equation.<BR>\n" );
document.write( "                              s=620 - 4.5t<BR>\n" );
document.write( "where s equals to average SAT score for a given year t equals time measured in year since 1985(t=0).<BR>\n" );
document.write( "(a) Identify the t and s intercept<BR>\n" );
document.write( "(b) Interpret the meaning of the intercepts. (Does your interpretation of the t intercept make sense)<BR>\n" );
document.write( "(c) Interpret the meaning of slope.<BR>\n" );
document.write( "(d) Sketch the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #483089 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=483089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=620+-+4.5t ALIGN=MIDDLE  ALT=\"s=620+-+4.5t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" >= average SAT score for a given year<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >= time measured in years since 1985 (t=0).<BR>\n" );
document.write( " <BR>\n" );
document.write( "(a) The s intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28620%29 ALIGN=MIDDLE  ALT=\"highlight%28620%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the s value when t=0.<BR>\n" );
document.write( "The t-intercept is the t value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=0 ALIGN=MIDDLE  ALT=\"s=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and is tthe solution to the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=620+-+4.5t ALIGN=MIDDLE  ALT=\"0=620+-+4.5t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=620+-+4.5t ALIGN=MIDDLE  ALT=\"0=620+-+4.5t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5t=620 ALIGN=MIDDLE  ALT=\"4.5t=620\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=620%2F4.5 ALIGN=MIDDLE  ALT=\"t=620%2F4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=1240%2F9%29 ALIGN=MIDDLE  ALT=\"highlight%28t=1240%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as an exact value, but the approximation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=138%29 ALIGN=MIDDLE  ALT=\"highlight%28t=138%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > would make a little more sense.<BR>\n" );
document.write( " <BR>\n" );
document.write( "(b) The meaning of the s-intercept is clear and makes sense. It is just the average SAT score for the year 1985, which was taken as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The t-intercept is an extrapolation that does not make much sense.<BR>\n" );
document.write( "It means that if the trend continued the average would reach zero in the year <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2123=1985%2B138 ALIGN=MIDDLE  ALT=\"2123=1985%2B138\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "It does not make sense to extrapolate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=138 ALIGN=MIDDLE  ALT=\"t=138\"   DISABLED_style= \"max-width:90%; height:auto;\" > a trend detected over a short range of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > values.<BR>\n" );
document.write( "The t range analyzed (time since 1985) cannot have been more than 2013-1985=28 years.<BR>\n" );
document.write( "It does not make sense to project a trend that far into the future.<BR>\n" );
document.write( "If we try to get more realistic, SAT scores were \"re-centered\" in the mid or late 1990's, and could be \"re-centered\" again in the next 110 years, so I would not take the current trend too seriously.<BR>\n" );
document.write( " <BR>\n" );
document.write( "(c) The slope of the trend line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.5 ALIGN=MIDDLE  ALT=\"-4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and can be interpreted as meaning that the average SAT score has been decreasing by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5 ALIGN=MIDDLE  ALT=\"4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > points per year.<BR>\n" );
document.write( "If we want to read more into the meaning of the slope, we could say that it illustrates the decline of education in the US.<BR>\n" );
document.write( "Or maybe we could say that as a larger percentage of high school students take the SAT from year to year, and/or apply to that college, the percentage of poorly prepared, low-scoring SAT takers has been increasing and driving down the average.<BR>\n" );
document.write( "Maybe the college as been attracting more and more low-scorers by doing too good a job of presenting itself as welcoming all students, and not being a \"selective\" institution.<BR>\n" );
document.write( " <BR>\n" );
document.write( "(d) Sketch the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C40%2C-100%2C800%2C%0D%0Agrid%280%29%2C%0D%0Aline%280%2C620%2C28%2C494%29%2Cline%2830%2C485%2C32%2C476%29%2C%0D%0Aline%2834%2C467%2C36%2C458%29%2Cline%2838%2C449%2C40%2C440%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );