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.

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

(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 part (a) result to find the function that models the instantaneous rate of change of the U.S. population.
(c) Find and interpret the instantaneous rates of change in 2000 and 2025.