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In 1920, the record for a certain race was 45.1 seconds. In 1950, it was 44.8 seconds. Let R(t)= the record in the race and t= the number of years since 1920. Find a linear function that fits the data. Find the year when the record will be 44.12 sec.
\n" ); document.write( ".
\n" ); document.write( "year| x-value | y-value
\n" ); document.write( "1920| 0 | 45.1
\n" ); document.write( "1950| 30 | 44.8
\n" ); document.write( ".
\n" ); document.write( "two points provided then is:
\n" ); document.write( "(0, 45.1)
\n" ); document.write( "(30,44.8)
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\n" ); document.write( "Slope:
\n" ); document.write( "(y2-y1)/(x2-x1)
\n" ); document.write( "(44.8-45.1)/(30-0)
\n" ); document.write( "(-0.3)/(30)
\n" ); document.write( "-0.01
\n" ); document.write( ".
\n" ); document.write( "using one point (0,45.1) and the slope -.01
\n" ); document.write( "plug into the \"point-slope\" form
\n" ); document.write( "y - y1 = m(x -x1)
\n" ); document.write( "y - 45.1 = -.01(x -0)
\n" ); document.write( "y - 45.1 = -.01x
\n" ); document.write( "y = -.01x+45.1
\n" ); document.write( ".
\n" ); document.write( "R(t)= -.01t+45.1
\n" ); document.write( ".
\n" ); document.write( "Now, to find when record will be 44.12 -- set it in place of R(t) and solve for t:
\n" ); document.write( "44.12 = -.01t+45.1
\n" ); document.write( "-0.98 = -.01t
\n" ); document.write( "98 = t (years after 1920)
\n" ); document.write( "answer then is
\n" ); document.write( "1920+98 = 2018\r
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