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# Consumer price index The Social Security Administration makes projections about the consumer price index (CPI) to understand the effects of inflation on Social Security benefits and to plan for cost-of-living increases. Suppose the rate of change of the CPI can be modeled with the function d C d t = 3.087 e 0.038 t dollars per year, where C is the consumer price index and t is the number of years past 1990. Does the model for the rate reflect the fact that the Social Security Administrations data (actual and projected for selected years from 1995 to 2070) in the table show that the CPI is increasing? Explain. Use integration and the tables data point for 2005 to find the function that models the Social Security Administrations CPI figures. Find and interpret C ( 35 ) and C ' ( 35 ) .

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### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042

#### Solutions

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### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042
Chapter 12.3, Problem 55E
Textbook Problem
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## Consumer price index The Social Security Administration makes projections about the consumer price index (CPI) to understand the effects of inflation on Social Security benefits and to plan for cost-of-living increases. Suppose the rate of change of the CPI can be modeled with the function d C d t = 3.087 e 0.038 t dollars per year, where C is the consumer price index and t is the number of years past 1990. Does the model for the rate reflect the fact that the Social Security Administrations data (actual and projected for selected years from 1995 to 2070) in the table show that the CPI is increasing? Explain. Use integration and the tables data point for 2005 to find the function that models the Social Security Administrations CPI figures. Find and interpret C ( 35 ) and C ' ( 35 ) .

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