document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=260292>Question 260292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 1920, the record for a certain race was 45.8 sec. In 1959, it was 44.9 sec. Let R(t)= the record in the race and t=the number of years since 1920\r<BR>\n" );
document.write( "\n" );
document.write( "Find a linear function that fits the data\r<BR>\n" );
document.write( "\n" );
document.write( "R(t)=<BR>\n" );
document.write( "What is the predictd record for 2003? sec.\r<BR>\n" );
document.write( "\n" );
document.write( "What is the predicted record for 2006\r<BR>\n" );
document.write( "\n" );
document.write( "In what year will the predicted record be 43.10 seconds\r<BR>\n" );
document.write( "\n" );
document.write( "Round to the nearest hundredth </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #191725 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=191725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We start with our coordinates in disguise:<BR>\n" );
document.write( "(1920, 45.8) and (1959,44.9), however, time is years \"since\" 1920, so we readjust to get<BR>\n" );
document.write( "(0, 45.8), (39, 44.9).<BR>\n" );
document.write( "step 1 - we can find the slope of these as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2844.9-45.8%29%2F%2839-0%29 ALIGN=MIDDLE  ALT=\"m+=+%2844.9-45.8%29%2F%2839-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-.9%2F39 ALIGN=MIDDLE  ALT=\"m+=+-.9%2F39\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-.0230769 ALIGN=MIDDLE  ALT=\"m+=+-.0230769\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 2 - using this slope and a coordinate, we can find the linear equation as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45.8+=+-.0230769%2A0+%2B+b ALIGN=MIDDLE  ALT=\"45.8+=+-.0230769%2A0+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45.8+=+b ALIGN=MIDDLE  ALT=\"45.8+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step p 3 - write the linear equation as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28t%29+=+-.0230769t+%2B+45.8 ALIGN=MIDDLE  ALT=\"R%28t%29+=+-.0230769t+%2B+45.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "find time for 2003? t = 83, so we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28t%29+=+-.0230769%2A%2883%29+%2B+45.8 ALIGN=MIDDLE  ALT=\"R%28t%29+=+-.0230769%2A%2883%29+%2B+45.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28t%29+=+43.88 ALIGN=MIDDLE  ALT=\"R%28t%29+=+43.88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "find time for 2006? t = 86, so we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28t%29+=+-.0230769%2A%2886%29+%2B+45.8 ALIGN=MIDDLE  ALT=\"R%28t%29+=+-.0230769%2A%2886%29+%2B+45.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28t%29+=+43.82 ALIGN=MIDDLE  ALT=\"R%28t%29+=+43.82\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "In what year will t = 43.10?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43.10+=+-.0230769t+%2B+45.8 ALIGN=MIDDLE  ALT=\"43.10+=+-.0230769t+%2B+45.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 45.8 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.7+=+-.0230769t ALIGN=MIDDLE  ALT=\"-2.7+=+-.0230769t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide by -0.0230769 to get<BR>\n" );
document.write( "t = 117<BR>\n" );
document.write( "or 2037. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );