The makeup of various groups within the U.S. population may reshape the electorate in ways that could change political representation and policies. By using U.S. Department of Labor data from 1980 and projected to 2050 for the civilian non-institutional population ages 16 and older, in millions, the population of those who are non-White or Hispanic can be modeled by the function
P(t) = 0.707t1.17 + 20.0
where t is the number of years past 1970.
(a) Find the function that models the instantaneous rate of change of the population of non-Whites or Hispanics.
(b) Find the function that models how fast the rate found in part (a) changes.
(c) Find and interpret P(55), P'(55), and P"(55).