Linearity and Time Invariance
As can be noticed in the table, the value of k is equal to the shift in time. After studying this table for a time, it becomes quite apparent that the function is not time invariant. This is due to the fact that, as time increases, so does k and therefore so does the amplitude of the function.
If the system is linear, then inputting the unit step function $ u[n] $ would yield the output.
