12. [-/1 Points] HARMATHAP12 9.4.061. The table gives the U.S. population to the nearest million for selected years from 1950 and projected to 2050. Year 1950 1960 1970 1980 1990 2000 Total 160 190 215 235 260 288 W 2010 315 2015 328 2020 343 2030 370 2040 391 2050 409 | ASK YOUR TEACH (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 coefcients. P(t) = (b) Use the part (a) result to find the function that models the instantaneous rate of change of the U.S. population. Report this model with three significant digit coefcients. P'(t) = (c) Find the instantaneous rates of change in 2000 and 2025. (Round your answers to two decimal places.) 2000 2025 Interpret these rates. In 2051, the U.S. In 2001, the U.S. In 2001, the U.S. In 2001, the U.S. In 2001, the U.S. Need Help? _' population will rise by about P'(50) million people. In 2076, the U.S. population will rise by about P'(75) million people. population will rise by about P'(75) people. In 2026, the U.S. population will rise by about P'(50) people, population will rise by about P'(75) million people. In 2026, the U.S. population will rise by about P'(50) million people. population will rise by about P'(50) million people. In 2026, the U.S. population will rise by about P'(75) million people. population will rise by about P'(50) people. In 2026, the U.S. population will rise by about P'(75) people