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 so much
You're welcome! To find the equation for the record in the race as a function of the number of years since 1920, we can use linear regression.
First, let's assign the variables:
- Let t represent the number of years since 1920.
- Let R(t) represent the record in the race at time t.
We have two data points:
- For t=0 (1920), R(t) = 45.1 seconds.
- For t=40 (1960), R(t) = 44.3 seconds.
Using these data points, we can set up a linear regression equation of the form R(t) = mt + b, where m represents the slope and b represents the y-intercept.
Using the slope formula:
m = (44.3 - 45.1) / (40 - 0) = -0.8 / 40 = -0.02
Next, we can substitute one of the data points to find the y-intercept:
45.1 = -0.02 * 0 + b
b = 45.1
Therefore, the equation for the record in the race is:
R(t) = -0.02t + 45.1
We can now use this equation to find the record for any given year since 1920. Just substitute the value of t into the equation R(t) = -0.02t + 45.1, and you'll get the corresponding record in the race.