document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155358>Question 155358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 1920, the record for a certain race was 46.8 sec. In 1980, the record was 45.6 sec. Let R(t) + the record in the race and t = the number of years since 1920.<BR>\n" );
document.write( "a) find a linear function that fits the data.<BR>\n" );
document.write( "b) What is the predicted record for 2003?<BR>\n" );
document.write( "c) What is the predicted record for 2006?<BR>\n" );
document.write( "In what year will the predicted record be 45.0 sec? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114423 by </B><A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><B>mangopeeler07(462)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><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=114423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In 1920, the record for a certain race was 46.8 sec. In 1980, the record was 45.6 sec. Let R(t)= the record in the race and t = the number of years since 1920.<BR>\n" );
document.write( "a) find a linear function that fits the data.<BR>\n" );
document.write( "b) What is the predicted record for 2003?<BR>\n" );
document.write( "c) What is the predicted record for 2006?<BR>\n" );
document.write( "In what year will the predicted record be 45.0 sec?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R(t)=record <BR>\n" );
document.write( "t=# years since 1920\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In 1920, the record for a certain race was 46.8 sec. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R(0)=46.8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In 1980, the record was 45.6 sec.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R(60)=45.6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y=f(x)<BR>\n" );
document.write( "y=mx+b\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Points:<BR>\n" );
document.write( "(0,46.8)<BR>\n" );
document.write( "(60,45.6)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "slope= (45.6-46.8)/(60-0)= -1.2/60  or -1/50\r<BR>\n" );
document.write( "\n" );
document.write( "y=(-1/50)x + b.<BR>\n" );
document.write( "46.8=(-1/50)0+b<BR>\n" );
document.write( "46.8=b\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a) find a linear function that fits the data.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x)=(-1/50)x+46.8<BR>\n" );
document.write( "---------------------------------------------------------<BR>\n" );
document.write( "b) What is the predicted record for 2003?<BR>\n" );
document.write( "x=2003-1920<BR>\n" );
document.write( "x=83\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(83)=(-1/50)83+46.8<BR>\n" );
document.write( "f(83)=45.14\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "45.14<BR>\n" );
document.write( "---------------------------------------------------------<BR>\n" );
document.write( "c) What is the predicted record for 2006?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x=2006-1920<BR>\n" );
document.write( "x=86<BR>\n" );
document.write( "f(86)=(-1/50)86+46.8<BR>\n" );
document.write( "f(86)=45.08\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "45.08<BR>\n" );
document.write( "---------------------------------------------------------<BR>\n" );
document.write( "In what year will the predicted record be 45.0 sec?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x)=45<BR>\n" );
document.write( "(-1.2/60)x+46.8=45<BR>\n" );
document.write( "(-1.2/60)x=-1.8<BR>\n" );
document.write( "x=90\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1920+90=2010\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2010 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );