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t the end of each year the faculty for a graduate program examine the progress that each graduate student has made on their required thesis.

t the end of each year the faculty for a graduate program examine the progress that
each graduate student has made on their required thesis. Past records indicate that
30% of graduate students complete the thesis requirement (C) and 10% are dropped
from the program for insufficient progress (D), never to return. The remaining students
continue to work on their theses and remain current graduate students (G).
(a) Construct a 3\times 3 matrix A that describes the student populations movement
within the graduate program over each one year period. Label the rows and
columns of A beginning with G and ending with D.
(b) Currently, there are 100 graduate students in the program and no students have
completed their thesis or been dropped from the program. Find an initial popu-
lation vector x0 for the graduate student population.
(c) Using A, predict how many students remain graduate students (G), have com-
pleted their thesis (C), and have been dropped from the program (D) one year
from now.
(d) Using A, predict how many students remain graduate students (G), have com-
pleted their thesis (C), and have been dropped from the program (D) two years
from now.
2

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