The chart below shows the world records for the women’s 10,000 meter run in the years 1970...

The chart below shows the world records for the women’s 10,000 meter run in the years 1970 and 1993.

For the years between 1970 and 1993, the world record can be approximated by the equation

where y is the world-record time (in seconds) in the year t. Use the given equation, the quadratic formula, and your calculator to estimate the year in which the record might have been 32 minutes (= 1920 seconds).

(As in Exercise, you’ll get two solutions for the quadratic; pick the appropriate one.) Then say by how many years your prediction is off, given the following information: On September 19, 1981, Yekena Sipatova of the former Soviet Union ran a record time of 32:17.2; in the following year on July 16, Mary Decker of the United States ran 31:35.3.

Exercise

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.