In 1920 the record for a certain race was 45.1 sec. In 1960, it was 44.3 sec. Let R(t)= the record in the race t= the number of years since 1920. Thank you for your help
You're welcome! To find an equation for the record in the race as a function of the number of years since 1920, we can use the given data as two points on a line.
Let's call the record in the race R(t), where t represents the number of years since 1920. We have two points: (0, 45.1) and (40, 44.3).
Now, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the first point (0, 45.1), we have:
R(t) - 45.1 = m(t - 0)
R(t) - 45.1 = mt
Now, let's find the slope (m) using the second point (40, 44.3):
m = (44.3 - 45.1) / (40 - 0)
m = -0.8 / 40
m = -0.02
So, the equation for the record in the race (R(t)) as a function of the number of years since 1920 (t) is:
R(t) = -0.02t + 45.1
This equation represents a linear relationship between the record in the race and the number of years since 1920.