A certain county in Nevada is one of the fastest-growing metropolitan areas in the United States. The population of this county from 1970 through 2010 is approximated by the function P(t) = 39,009t3 − 77,394t2 + 234,633t + 273,288 (0 ≤ t ≤ 4)
where t is measured in decades, with t = 0 corresponding to the beginning of 1970.
1. Find when the population is increasing or decreasing at the slowest pace. Hint: Find the inflection point of P in the interval (0, 4). (Round you answer to two decimal places.)
t=
2. Was the population of the county always increasing or decreasing over the time penod in question.
a. increasing
b. decreasing
c. varies