Each year at Manitoba High School, the teachers sit on a committiee.
Currently:
• 30% are on the Sports committee.
• 20% are on the Arts committee.
• 50% are on the Graduation committee.
At the end of the school year, the teachers can change committees. Here are the changes that took place last June:
• 10% of the teachers from each committee stayed on their committee.
• 15% of the Sports committee joined the Graduation committee.
• 5% of the Arts committee joined the Sports committee.
• 30% of the Graduation committee joined the Arts committee.
(a) Create a transition matrix which shows the changes in committees. Be certain to include the labels "From" and "To."
(b) What percent of the teachers will be on the Sports committee two years from now?
(c) If these trends continue, determine the percentage of teachers on each committee once it stabilizes. Provide proof of stabilization.
Solution