Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. Consumer Price Index (CPI) can be modeled by the function

C(t) = 92.7 e^0.0271 

t where t is the number of years past 2010. With the reference year as 2012, a 2015 CPI = 106.15 means that goods and services costing $100.00 in 2012 cost $106.15 in 2015.

(a) Find the function that describes how fast the CPI model C(t) is changing.

(b) Find the instantaneous rate of change of the CPI model in 2010 and 2025.

(c) From part (b), interpret the rate for 2025.