With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate of change of U.S. population P can be modeled by dP = -0.0002187t2 + 0.0276t + 1.98 dt million people per year, where t = 0 represents the year 1960. (a) During what year does this rate of change reach its maximum? (b) In 1960, the U.S. population was 181 million. Use this to find a model for P(t). (Enter exact numerical values. Do not round.) P(t) = (c) For 2025, the Census Bureau's predicted U.S. population is 348 million. What population does the model predict? (Round your answer to the nearest million.) million

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
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With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate of change of U.S. population P can be modeled by
dP
-0.0002187t2 + 0.0276t + 1.98
dt
million people per year, where t = 0 represents the year 1960.
(a) During what year does this rate of change reach its maximum?
(b) In 1960, the U.S. population was 181 million. Use this to find a model for P(t). (Enter exact numerical values. Do not round.)
P(t) =
(c) For 2025, the Census Bureau's predicted U.S. population is 348 million. What population does the model predict? (Round your answer to the nearest million.)
million
Transcribed Image Text:With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate of change of U.S. population P can be modeled by dP -0.0002187t2 + 0.0276t + 1.98 dt million people per year, where t = 0 represents the year 1960. (a) During what year does this rate of change reach its maximum? (b) In 1960, the U.S. population was 181 million. Use this to find a model for P(t). (Enter exact numerical values. Do not round.) P(t) = (c) For 2025, the Census Bureau's predicted U.S. population is 348 million. What population does the model predict? (Round your answer to the nearest million.) million
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