Disposable income is the amount available for spending and saving after taxes have been paid and is one gauge for the state of the economy. By using U.S. Energy Administration data for selected years from 2010 and projected to 2040, the total U.S. disposable income, in billions, can be modeled by
D(t) = 10,020e0.02292t
where t is the number of years past 2010.
(a) Find the function that models the rate of change of disposable income.
(b) Find and interpret D(20) and D'(20).