The table gives the U.S. population to the nearest million for selected years from 1950 and projected

Question:

The table gives the U.S. population to the nearest million for selected years from 1950 and projected to 2050.

Total Total Year Year 1950 160 2010 315 1960 328 190 2015 2020 2030 1970 215 343 1980 235 370 1990 260 2040 391 2000 288

(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 1950. Report the model with three significant digit coefficients.
(b) Use the reported model to 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'(70) and P"(70).