Two competing companies offer cable television to a city with 100,000 households. Gold Cable Company has 10,000 subscribers and Galaxy Cable Company has 15,000 subscribers. The percent changes in cable subscriptions each year are shown in the matrix below $\left[ \begin{array} { l l l }
0.80 & 0.25 & 0.20 \
0.15 & 0.50 & 0.05 \
0.05 & 0.25 & 0.75
\end{array} \right]$ where the columns are percent changes from Gold, from Galaxy, and from Nonsubscriber respectively and the rows are percent changes to Gold, to Galaxy, and to Nonsubscriber respectively. Find the number of nonsubscribers in two years using matrix multiplication.

Question

Two competing companies offer cable television to a city with 100,000 households. Gold Cable Company has 10,000 subscribers and Galaxy Cable Company has 15,000 subscribers. The percent changes in cable subscriptions each year are shown in the matrix below $\left[ \begin{array} { l l l } 
0.80 & 0.25 & 0.20 \
0.15 & 0.50 & 0.05 \
0.05 & 0.25 & 0.75
\end{array} \right]$ where the columns are percent changes from Gold, from Galaxy, and from Nonsubscriber respectively and the rows are percent changes to Gold, to Galaxy, and to Nonsubscriber respectively. Find the number of nonsubscribers in two years using matrix multiplication.

Quizplus · Accepted Answer

The initial state vector is [10,000, 15,000, 75,000]. After two years of applying the transition matrix, the number of nonsubscribers is approximately 49,900.

Two Competing Companies Offer Cable Television to a City with 100,000