26. 0.18/0.37 points | Previous Answers TanApCalcBr10 4.2.099 My Notes Ask Your Teacher 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) 38,251t3-76,394t2+234,633t273,288 (0sts 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) increasing O decreasing varies (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 places.)
Show transcribed image text26. 0.18/0.37 points | Previous Answers TanApCalcBr10 4.2.099 My Notes Ask Your Teacher 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) 38,251t3-76,394t2+234,633t273,288 (0sts 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) increasing O decreasing varies (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 places.)