The Social Security Administration makes projections about the consumer price index (CPI) in order 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

dollars per year, where C is the consumer price index and t is the number of years past 1990.
(a) Does the model for the rate reflect the fact that the Social Security Administration's data (actual and projected for selected years from 1995 to 2070) in the table show that the CPI is increasing? Explain.
(b) Use integration and the table's data point for 2005 to find the function that models the Social Security Administration's CPI figures.
(c) Find and interpret C(35) and C(35).

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dC 3.087e dt 3.087e0.0384r 0.0384t Year CPI Year CPI 1995 100.00 2035 465.98 2000 118.21 2040 2045 566.94 2005 143.67 689.77 2010 174.80 2050 839.21 2015 212.67 2055 1021.02 2020 258.74 2060 1242.23 2025 314.80 2065 1511.36 2030 383.00 2070 1838.81