3. Orcas are long-lived marine mammals that live in stable social groups called "pods." Brault and Caswell (1993) used the 1973-1987 data from the coastal waters of British Columbia and Washington state and a stage-structured matrix model to investigate several demographic questions concerning the orcas. They model the females with a mixed age-stage classification: yearlings, juveniles (past the first year, but not yet mature), mature, postreproductive. The projection matrix is given by $$ A=\left [\begin{array}{cccc} 0 & 0.0043 & 0.1132 & 0W 0.9775 & 0.9111 & 0 & 0W 0 & 0.0736 & 0.9534 & 0W 0 & 0 & 0.0452 & 0.9804 \end{array} ight] $$ Use $R$ (or another program) to write a script file that a) computes the dominant eigenvalue $\lambda$ and stable stage distribution w for the whale population; b) projects the population dynamics for the next 50 years assuming that the current population vector is $x_{0}=(10,60,110,70)$ c) plots (using $\mathrm{R}$ or another program) on three separate graphs the projected changes over time in the total population $N(t)$ in year $t .$ the annual population growth rate $\frac{N(t+1)}{(t)}$. the proportion of individuals in each stage. S.P.PB. 260