Below is a table of the men's metric world track records as of August 1976 [Source: Guinness Book of World Records]. At that time, the mile was still a major track event contested by the world's best runners.
| Metric World Records (August 1976) x meters
| T secs
| Year set
| 100
| 9.96
| 68
| 200
| 19.81
| 71
| 400
| 43.9
| 68
| 800
| 103.5
| 76
| 1,000
| 133.9
| 74
| 1,500
| 212.2
| 74
| 2,000
| 291.4
| 76
| 3,000
| 455.2
| 74
| 5,000
| 793.0
| 72
| 10,000
| 1,650.8
| 73
| 20,000
| 3,444.2
| 76
| 25,000
| 4,456.8
| 75
| 30,000
| 5,490.4
| 70
| | ||
If you were an analyst back in 1976 and you had this data, could you use mathematics to make a prediction giving an accurate estimate of what the mile record would be in August 1976?
In this activity, based on "Estimating the Mile Record" [Peter Taylor, Calculus: The Analysis of Functions, Wall & Emerson], you will use increasingly sophisticated mathematical analysis to make better and better estimates. In conclusion, you will compare your estimates to the actual mile record for 1976 and see how your predictions measure up. Note: A mile equals about 1,609.344 meters.
First Analysis.
Note that since a mile is more than 1,500 meters, and less than 2,000 meters, the mile record should be between the records for these two distances. Based on this elementary analysis, fill out the table below:
| Your Lower Bound for mile record: | ____________________ seconds. |
| Your Upper Bound for mile record: | ____________________ seconds. |
| The size of your "Uncertainty Gap": | ____________________ seconds. |