State cigarette taxes the average state cigarette tax per

Question

Question: State cigarette taxes the average state cigarette tax per pack (in dollars) from 2001 through 2007 is approximated by the function

T(t) = 0.43t^0.43          (1 ≤ t ≤ 7)

Where t is measured in years, with t = 1 corresponding to the beginning of 2001.

A. Show that the average state cigarette tax per pack was increasing throughout the period in question.

B. What can you say about the rate at which the average state cigarette tax per pack was increasing over the period in question?