40 new students come to a class each year. At the end of the year, 10% of the students leave the school, 30% stay in the class and repeat the next year, and 10% stay at the end of the second year and repeat the course.

Question

40 new students come to a class each year. At the end of the year, 10% of the students leave the school, 30% stay in the class and repeat the next year, and 10% stay at the end of the second year and repeat the course.
a) Set up the difference equation.
b) Determine the transfer function of the system.
c) How many students will be in the classroom after 5 years?
d) What will be the maximum number of students in the class?