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)=38,143t^3 - 76,394t^2 + 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 increasing or decreasing over the period of time in question? (Hint: Show that P’(t)> 0 for all t in the interval (0,4) 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 your answer to two decimal places.)
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)=38,143t^3 - 76,394t^2 + 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 increasing or decreasing over the period of time in question? (Hint: Show that P’(t)> 0 for all t in the interval (0,4) 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 your answer to two decimal places.)
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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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)=38,143t^3 - 76,394t^2 + 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 increasing or decreasing over the period of time in question? (Hint: Show that P’(t)> 0 for all t in the interval (0,4)
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 your answer to two decimal places.)
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