Have you or a friend ever run in a 10K (10,000 meter) race? When one of the authors poll...

Have you or a friend ever run in a 10K (10,000 meter) race? When one of the authors polled his large precalculus class, he found that there were five (out of 160) students who said that they had run a 10K under 50 minutes. Of those five, two (one male, one female) said they had run a 10K in under 40 minutes. The world record for this event is well under 30 minutes. In this exercise you’ll look at some of the world records in this event over the past decade.

(a) The table that follows lists the world records in the (men’s) 10,000 meter race as of the end of the years 1996, 2000, and 2004. After converting the times into seconds, plot the three points corresponding to these records in a coordinate system similar to the one shown.

(b) Use the midpoint formula and the data for 1996 and 2000 to compute an estimate for what the world record might have been by the end of 1998. Then compute the percentage error (rounded to two decimal places), given that the record at the end of 1998 was 26:22.75 (set by Haile Gebreselasie on August 4, 1998). Was your estimate high or low?

(c) Use the midpoint formula and the data for 2000 and 2004 to compute an estimate for what the world record might have been by the end of 2002. Then compute the percentage error given that the record at the end of 2002 was still the 26:22.75 set by Haile Gebreselasie in 1998. Was your estimate high or low? Is the percentage error more or less than that obtained in part (b)?

(d) Using a coordinate system similar to the one shown in part (a), or using a photocopy, plot the points corresponding to the (actual, not estimated) world records for the years 1996, 1998, 2000, 2002, 2004, and 2006. Except for 2006, all the records have been given above. The world record at the end of 2006 was 26:17.53 (set by Kenenisa Bekele Aug. 26, 2005). Use the picture you obtain to say whether or not the record times seem to be leveling off. (Note: Bekele’s record still stood in 2008.)