Consider a species of bird that can be split into three age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years. The population is observed once a year. Given that the Leslie matrix is equal to $$L = {\left[\begin{array}{ccc} 0 &2 &1\cr 0.2 &0 &0\cr 0 &0.5 &0 \end{array}\right]}$$ and the initial population distribution is: 1200 of the first age group, 2000 of the second age group, and 2400 of the oldest age group, answer the following questions. The initial population vector is $\mathbf{x}_0 =$$\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$. How many birds aged 1-2 years are there after 10 years? How many birds aged 0-1 years are there after 20 years? How many birds are there after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. $\lambda_1\ =\ $ What is the long-term growth rate of this population of birds as a percent? Growth rate =
(The growth rate is the percentage of growth over/under 100%.) Are the birds thriving, static, or going extinct? ? going extinct static thriving