Chapter 12.1, Problem 56E

Consumer prices The consumer price index (CPI) measures how prices have changed for consumers.

With 1995 as a reference of 100, a year with $\text{CPI = 150}$ indicates that consumer costs in that year were 1.5 times the 1995 costs. With U.S. Department of Labor data for selected years from 1995 and projected to 2050, the rate of change of the CPI can be modeled by

$\frac{dC}{dt}=0.009t^2-0.096t+4.85$ dollars per year, where t = 0 represents 1990.

(a) Find the function that models C(t) if the CPI was 175 in 2010.

(b) What does the model from part (a) predict for the consumer costs in 2030? How does this compare to 2010?