The chart that follows shows the world records for the men’s 10,000 meter run in the yea...

The chart that follows shows the world records for the men’s 10,000 meter run in the years 1972 and 1998.

For the years between 1972 and 1998, the world record can be approximated by the equation

where y is the world-record time (in seconds) in the year t.

(a) Use the given equation, the quadratic formula, and your calculator to estimate the year in which the record might have been 27 minutes (=1620 seconds). (You’ll get two solutions for the quadratic; be sure to pick the appropriate one.) Then say by how many years your prediction is off, given the following information: On July 5, 1993, Richard Chelimo of Kenya ran a record time of 27:07.91; five days after that, Yobes Ondieki, also of Kenya, ran 26:58.38.

(b) Estimate the year in which the record might have been 26:30 (= 1590 seconds). Then say by how many years your prediction is off, given the following information: On July 4, 1997, Haile Gebrselassie ran a record time of 27:07.91; eighteen days later, Paul Tergat of Kenya ran 26:27.85.

(c) It is interesting to see how accurately (or inaccurately) the quadratic approximating equation predicts record times outside its specified domain. In August 2005, Kenenisa Bekele of Ethiopia ran a record time of 26 minutes 17.54 seconds. (This was still the record in 2008.) In what year does the equation predict this time would be achieved? How many years off the actual date is the prediction?