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anonymous

  • 5 years ago

In 1920, the record for a certain race was 45.7 sec. In 1970, it was 44.7 sec. Let R(t) = the record in the race and t= the number of years since 1920. a- Find the linear function that fits the data b- Use the function in (a) to predict the record for 2003 and in 2006 c- Find the year when the record will be 43.94 sec.

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  1. anonymous
    • 5 years ago
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    a) Since the question asks for a linear function that gives us a hint that we want a straight line (y=mx+b). So you first need to find the slope: m=(y2-y1)/(x2-x1)= (44.7-45.7)/(50-0)=-1/50=-0.02 Then we need to find our y-intercept (b), so we will use x=0 and y=50 which will represent the 1920 record: 50=-0.02(0)+b 50=b Therefore, your linear function will be y=-0.02x+50 b) For the 2003 (2003-1920=83 years since 1920), plug in 83 for x. Likewise for the 2006 record plug in 86 for x. c) Set y=43.94. So your equation looks like this: 43.94=-0.02x+50 Then solve for x: (43.94-50)/(-0.02)=x

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