Final answer:
To model the world record for the Men's Mile Race since 1960, a linear equation y = -0.005t + 3.91 can be used, where y is the record time in minutes and t is the number of years since 1960. Using this model, the estimated record time is 3.71 minutes for 2000 and 3.61 minutes for 2020.
Step-by-step explanation:
To write a linear model that represents the world record for the Men's Mile Race as a function of the number of years since 1960, we can use the two given data points: in 1960, the record was 3.91 minutes, and in 1980, it was 3.81 minutes. Let's denote the year as t, where t=0 corresponds to the year 1960. Thus, in 1980, t=20 years have passed since 1960.
First, we find the slope m of the line using the formula m = (y2 - y1)/(x2 - x1), which gives us:
m = (3.81 - 3.91)/(20 - 0) = -0.005 minutes per year.
Now, the linear equation will have the form: y = mt + b, where y is the world record time and b is the y-intercept. Since we know that in 1960 (t=0), the record was 3.91 minutes, thus b=3.91.
The linear model is: y = -0.005t + 3.91.
To estimate the record time in 2000:
t = 2000 - 1960 = 40
y = -0.005(40) + 3.91 = 3.71 minutes.
To predict the record time in 2020:
t = 2020 - 1960 = 60
y = -0.005(60) + 3.91 = 3.61 minutes.