Prices for goods and services tend to rise over time, and this results in the erosion of purchasing power. With the 2012 dollar as a reference, purchasing power of 0.921 for a certain year means that in that year, a dollar will purchase 92.1% of the goods and services that could be purchased for $1 in 2012. Using Social Security Administration data for selected years from 2012 and projected to 2050, the purchasing power of a 2012 dollar can be modeled by the function

P(t) = 1.078(0.9732^t)

where t is the number of years past 2010.

(a) Find the function that models the rate of change of the purchasing power of a 2012 dollar.

(b) Find and interpret P(18) and P'(18).