Personal income suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by
dI/dt = 33.68e0.0676t
where t is the number of years past 1960.
(a) Is the average rate of change of total personal income from 2005 to 2008 found from the data in the table a better estimate for the instantaneous rate for 2005 or for 2008?
(b) Use the data point for 1970 to find the function that models I(t).
(c) Find and interpret I(55) and I'(55).
