document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201381>Question 201381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! I need a help with ASAP!!!<BR>\n" );
document.write( "Problem 1.<BR>\n" );
document.write( "In 1920, the record for a certain race was 45.4 sec. In 1990, it was 44.0 sec.<BR>\n" );
document.write( "Let R(t)= the record in the race and t= the number of the year since 1920.<BR>\n" );
document.write( " <BR>\n" );
document.write( "a) Find a linear function that the date<BR>\n" );
document.write( "b) Use the function in (a) to predict the record in 2003 and in 2006.<BR>\n" );
document.write( "c) Find the year when the record will be 43.56 sec<BR>\n" );
document.write( " <BR>\n" );
document.write( "Find a linear function that fits the data.<BR>\n" );
document.write( "R(t)= ?? -002-45.4???<BR>\n" );
document.write( "What is the predicted record for 2003? 43.74??<BR>\n" );
document.write( "What is the predicted record for 2006? 43.68??<BR>\n" );
document.write( "In what year will the predicted record be 43.56 sec??<BR>\n" );
document.write( " <BR>\n" );
document.write( "I appreciate this.<BR>\n" );
document.write( "Thank you!  <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 #151614 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=151614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In 1920, the record for a certain race was 45.4 sec. In 1990, it was 44.0 sec.<BR>\n" );
document.write( "Let R(t)= the record in the race and t= the number of the year since 1920.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "a) Find a linear function that the date<BR>\n" );
document.write( "Think of the x-axis representing the year and the y-axis representing the \"record-time\" in seconds.<BR>\n" );
document.write( "The problem, then, really gives you two data points: (remember, since 1920)<BR>\n" );
document.write( "1920 we get: (0,45.4)<BR>\n" );
document.write( "1990 we get: (70,44)<BR>\n" );
document.write( "Slope then is <BR>\n" );
document.write( "(y2-y1)/(x2-x1) = (44-45.4)/(70-0) = -1.4/70 = -0.02<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using the slope and one (70,44) of the two points substitute it into the \"point-slope\" form:<BR>\n" );
document.write( "y-y1 = m(x-x1)<BR>\n" );
document.write( "y-44 = -0.02(x-70)<BR>\n" );
document.write( "y = -0.02(x-70) + 44<BR>\n" );
document.write( "y = -0.02x + 1.4+44<BR>\n" );
document.write( "y = -0.02x + 45.4<BR>\n" );
document.write( "Replacing y with R(t) and x with t we get:<BR>\n" );
document.write( "R(t) = -0.02t + 45.4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b) Use the function in (a) to predict the record in 2003 and in 2006.<BR>\n" );
document.write( "For 2003:<BR>\n" );
document.write( "t = 2003-1920 = 83<BR>\n" );
document.write( "R(t) = -0.02t + 45.4<BR>\n" );
document.write( "R(t) = -0.02(83) + 45.4<BR>\n" );
document.write( "R(t) = -1.66 + 45.4<BR>\n" );
document.write( "R(t) = -1.66 + 45.4<BR>\n" );
document.write( "R(t) = 43.74 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For 2006:<BR>\n" );
document.write( "t = 2006-1920 = 86<BR>\n" );
document.write( "R(t) = -0.02t + 45.4<BR>\n" );
document.write( "R(t) = -0.02(86) + 45.4<BR>\n" );
document.write( "R(t) = -1.66 + 45.4<BR>\n" );
document.write( "R(t) = -1.72 + 45.4<BR>\n" );
document.write( "R(t) = 43.68 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c) Find the year when the record will be 43.56 sec<BR>\n" );
document.write( "R(t) = -0.02t + 45.4<BR>\n" );
document.write( "43.56 = -0.02t + 45.4<BR>\n" );
document.write( "43.56-45.4 = -0.02t<BR>\n" );
document.write( "-1.84 = -0.02t<BR>\n" );
document.write( "92 = t<BR>\n" );
document.write( "Year then = 1920+92 = 2012<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );