Population The resident population P (in millions) of the United States from 2000 through 2013 can be modeled by $P=-0.00232{t}^{3}+0.0151{y}^{2}+2.83t+281.8,0\le t\le 13,$
where $t=0$ corresponds to 2000.

(Source: U.S. Census Bureau)

Make a conjecture about the maximum and minimum
populations of the United States from 2000 to 2013.

Analytically find the maximum and minimum populations over
the interval.

The brief paragrah while comparing a conjecture with the minimum population was 281.8
million in 2000 and the maximum population was 316.1 million in 2013.

We need to calculate: The absolute extrema of the popullation $P=-0.00232{t}^{3}+0.0151{y}^{2}+2.83t+281.8,0\le t\le 13$ over the closed interval [0, 13].