Question: Alternative minimum tax congress created the alternative minimum tax (amt) in the late 1970s to ensure that wealthy people paid their fair share of taxes. But because of quirks in the law, even middle-income taxpayers have started to get hit with the tax. The amt (in billions of dollars) projected to be collected by the irs from the beginning of 2001 through 2010 is
f(t) = 0.0117t3 + 0.0037t2 + 0.7563t + 4.1 (0 ≤ t ≤ 9)
Where t is measured in years, with t 0 corresponding to 2001 .
A. Show that f is increasing on the interval (0, 9). What does this result tell you about the projected amount of amt paid over the years in question?
B. Show that f is increasing on the interval (0, 9). What conclusion can you draw from this result concerning the rate of growth at which the amt is paid over the years in question?