In Exercise 41, the market share of Company A in future years can be found by multiplying by the transition matrix T repeatedly. What would the market share of Company A be after 3 years?

Data from Exercises 41

From past records, satellite television Company A finds that among its current customers, 92% will still be a customer one year from now and the remaining 8% will be lost to other competing companies. Also, among customers who are currently with other companies, 14% will switch to Company A within one year and the remaining 86% will remain with other companies. This is represented by the following transition matrix T:

Company A currently has 40% of the market share, given by

Find the market share of Company A after one year by multiplying

Transcribed Image Text:

Now A Other One year from now A Other 0.92 0.08 0.14 0.86 = T