An indecisive student contemplates whether he should stay ho

An indecisive student contemplates whether he should stay home or take his final exam, which is being held 2 miles away. Starting at home, the student travels half the distance to the exam location before changing his mind. The student turns around and travels half the distance between his current location and his home before changing his mind again. This process of changing direction and traveling half the remaining distance continues until the student either reaches a destination or dies from exhaustion.

a. Determine a suitable difference equation description of this system.

b. Use MATLAB to simulate the difference equation in part (a). Where does the student end up as n ? How do your answer change if the student goes two-thirds the way each time, rather than halfway?

c. Determine a closed-form solution to the equation in part (a). Use this solution to verify the results in part (b).

Solution

A. An indecisive student contemplates whether he should stay home or take his final exam,
which is being held 2 miles away. Starting at home, the student travels half the distance
to the exam venue before changing his mind. The student turns around and travels half
the distance between his current location and his home before changing his mind again.
This process of changing direction and traveling half the remaining distance continues
until the student reaches a certain destination.