Question: In 1958, L. Lucy developed a method for predicting the world record for any given year that a human could run a distance of 1

In 1958, L. Lucy developed a method for predicting the world record for any given year that a human could run a distance of 1 mile. His formula is given as follows:

where t(n) is the world record (in seconds) for the mile run in year 1950 + n. Thus, n = 5 corresponds to the year 1955.

a. Find the estimate for the world record in the year 2010.

b. Calculate the instantaneous rate of change for the world record at the end of year 2010 and interpret.

c. Find

and interpret. How does this compare with the current world record?

t(n) = 218 +31(0.933)",

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