Chapter 2, Problem 3RP

Explanation of Solution

Relating two vectors:

Suppose that $U_t$ be the number of untenured State University faculty at the beginning of the year $t$, and $T_t$ be the tenured number.

Since 75% of the untenured faculty remains untenured at the beginning of the year t+1.

Thus, the number of untenured faculty in the beginning of the year t+1 is given below:

$U_{t+1}=0.75U_t$

Also, 20% of all untenured faculties become tenured and 90% of the tenured faculty remains tenured at the beginning of the year t+1.

Therefore, the number of tenured faculties in the beginning of the year t+1 is as follows:

$T_{t+1}=0.2U_t+0$