Modeling  U.S. Population

The table gives the U.S. population to the nearest million (actual or projected) for selected years. 

(a) Find a cubic function P(t) that models these data, where P is the U.S. population in millions and t is the number of years past 1960.

(b) Find the function that models the instantaneous rate of change of the U.S. population.

(c) Use the second derivative to determine how fast this rate was changing in 2000 and 2020.

(d) Write sentences that explain the meanings of P'(60) and P"(60).