The consumer price index (CPI) measures how prices have changed for consumers. With 1995 as a reference of 100, a year with CPI = 150 indicates that consumer costs in that year were 1.5 times the 1995 costs. With labor data from a country for selected years from 1995 and projected to 2050, the rate of change of the CPI can be modeled by [tex]\frac{dC}{dt} = 0.009t^2 - 0.096t + 4.85[/tex] dollars per year, where t=o represents 1990.
Find the function that models C(t), if the CPI was 160 in 2010.