Question: Population growth in clark county clark county in nevada-dominated by greater las vegas-is one of the fastest-growing metropolitan areas in the united states. The population of the county from 1970 through 2000 is approximated by the function
P(t) = 44560t3 - 89394t2 + 234633t + 273288 (0 ≤ t ≤ 4)
Where t is measured in decades, with t 0 corresponding to the beginning of 1970.
A. Show that the population of clark county was always increasing over the time period in question. Hint: show that p'(t) > 0 for all t in the interval (0, 4).
B. Show that the population of clark county was increasing at the slowest pace some time toward the middle of august 1976.