Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to
and the initial population distribution is of the first age group, of the second age group, of the third group, and of the oldest age group, answer the following questions.

The initial population vector is
.

How many elk aged 1-2 years are there expected to be after 10 years?

How many elk aged 0-1 years are there expected to be after 20 years?

How many elk are there expected to be after 30 years?

Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places.

What is the long-term growth rate of this population of elk as a percent? growth rate = (The growth rate is the percentage of growth over/under 100%.)