By using Social Security Administration data for selected years from 2012 and projected to 2050, the rate of change of the total U.S. taxable payroll can be modeled by dP/dt = 27.0t + 112 billions of dollars per year, where t is the number of years past 2010.
(a) If total U.S. taxable payroll is $7088 billion in 2016, find the function P(t). Use three significant digits.
(b) What does P(t) predict for the total U.S. taxable payroll in 2025?