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Population Growth in Clark County A certain county in Nevada is one of the fastest-growing...

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Population Growth in Clark County A certain county in Nevada is one of the fastest-growing metropolitan areas in the United States. The population of this county from 1 approximated by the functionP(t) = 43,059t - 86,394t2 + 234,633t + 273,288(0 ? t ? 4)where t is measured in decades, with t= 0 corresponding to the beginning of 1970.(a) Was the population of the county always increasing or decreasing over the time period in question. Hint: Show that P'(t) > 0 for all t in the interval (0, 4).increasingdecreasingvaries(b) 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 placet=

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