anonymous
  • anonymous
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.
Mathematics
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anonymous
  • anonymous
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.
Mathematics
chestercat
  • chestercat
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
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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