The matrix A shown below is a Leslie matrix for projecting the female population of Argentina. There are three age groups, each 18 years wide. The starting population for 1992 includes 3.9 million girls aged 0 to 18, 3.3 million women aged 18 to 36, and 2.8 million women aged 36 to 54.

0.551 0.556 0.037 A = 0.962 0 0 0 0.909 0 (a) How long is the interval of time covered by a single projection step? (b) What is the total population of women up to age 54 after one pro j ection step? (c) What is the total population of women up to age 5 4 after three projection steps? To what year would this total apply? (d) At what rate would the population of Argentina be growing ac- cording to this projection over three projection steps