Using U.S. Energy Information Administration data for selected years from 2010 and projected to 2040, theHarMachkpi211.2.065. U.S. real disposable income per capita (in thousands of dollars) can be modeled byI(t)=32.11(1.014)twhere t is the number of years after 2010.(a) Write the function that models the rate of change of U.S. per capita real disposable income (in thousands of dollars/year).(Round your coefficients to four decimal places.)r(t)=(b) Predict the rate of change (in thousands of dollars/year) of U.S. per capita real disposable income in 2036.(Round your answer to four decimal places.)5 x thousand/year