Dolphins can be divided into three age groups. Young (0-5 years old), adult (5-10 years old), and elderly (10+ years old). Young dolphins have a 65% chance of surviving to the next age group. Adult dolphins have a 78% chance of surviving to the elderly age group and their fertility rate is 120% every five years. Elderly dolphins have a 20% chance of surviving for another 5 years and their fertility rate is 15% every five years.

A) Create a stage diagram for the population.

B) Create a transition matrix.

C) If the population begins with 1000 adult dolphins, what will the population look like after 25 years for each age group? Include the growth equation for each age group.

D) Whats the dominant eigenvalue and eigenvector? What does this show over time about the dolphin population?