Each year, 20% of all untenured State University faculty become tenured, 5% quit, and 75% remain untenured. Each year, 90% of all tenured S. U. faculty remain tenured and 10% quit. Let U_t be the number of untenured S. U. faculty at the beginning of year t, and T_t the tenured number. Use matrix multiplication to relate the vector [U_t + 1 T_t + 1] to the vector [U_t T_t].

Question

Mathematics

Bailey Ward

2 January, 03:39

Each year, 20% of all untenured State University faculty become tenured, 5% quit, and 75% remain untenured. Each year, 90% of all tenured S. U. faculty remain tenured and 10% quit. Let U_t be the number of untenured S. U. faculty at the beginning of year t, and T_t the tenured number. Use matrix multiplication to relate the vector [U_t + 1 T_t + 1] to the vector [U_t T_t].

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Bridger Reeves · Answer 1

Step-by-step explanation:

(Ut + 1) = (Ut Tt) (a b)

(T1 + 1) (c d)

a = Untenured to untenured = 0.75

c = tenured to untenured = 0

b = untenured to tenured = 0.20

d = tenured to tenured = 0.90

(Ut + 1) = (Ut Tt) (0.75 0.20)

(T1 + 1) (0 0.90)