Suppose certain animal has a maximum life span of 3 years. A year 1 (01- year) female has no offspring; a year 2 (12-years) female has 3 daughters on the average; and a year 3 (23-years) female has a mean of 2 daughters. Thirty percent of year 1 animals live to year 2, and 40% of year 2 animals live to year 3. Suppose the numbers of year 1, 2, and 3 females are 2030, 652, and 287, respectively.

a. Determine the corresponding Leslie matrix, L.

b. Give the initial female population distribution vector x(0).

c. Calculate the population distribution at time t = 1, vector x(1).

d. Calculate the class percentages of the total population at time t = 1.

e. Give the vector for class percentages of the total population, v, expressed to two decimal places, to which x(t)/T(t) converges, where T(t) is the total population at time t.

f. Find the number , expressed to two decimal places, to which x(t + 1)/x(t) converges.

g. Using answers from Parts a, d, and f, verify that Lv = v.