Chapter 12.1, Problem 55E

U.S. population With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate of change of U.S. population P can be modeled by

$\frac{dp}{dt} =—0.0002187t^2+0.0276t+1.98$ million people per year, where t - 0 represents 1960.

(a) In what year does this rate of change reach its maximum?

(b) In 1960, the U.S. population was 181 million. Use this to find a model for P(t).

(c) For 2025, the Census Bureaus predicted U.S. population is 348 million. What does the model predict?