The 2009 Kentucky Derby was won by the horse named Mine That Bird (at more than 50:1 odds) in time of 2:02.66 (2 minutes and 2.66 seconds) for 1.25 -mile race. Times at the quarter-mile, half-mile, and mile poles were 0:22.98, 0:47.23, and 1:37.49.
a. Use such values together with the starting time to develop a natural cubic spline for Mine That Bird's race.
b. Use the spline to predict the time at the three-quarter-mile pole, and compare this to the actual time of 1:12.09.
c. Use the spline to approximate Mine That Bird's starting speed and speed at the finish line.