Which one of the following options is correct for the given data in the table?

Let us check the relations given in the options for each iteration $i > 0$:

1. For $X(i)$:

   • At $i = 1$: $X(1) = 16 = 20 + (-4) = X(0) + I(1)$

   • At $i = 2$: $X(2) = 26 = 16 + 10 = X(1) + I(2)$

   • At $i = 3$: $X(3) = 41 = 26 + 15 = X(2) + I(3)$

   Thus, the recurrence relation for $X(i)$ is:

   $$X(i) = X(i - 1) + I(i), \quad i > 0$$

2. For $Y(i)$:

   • At $i = 1$: $Y(1) = -80 = 20 \times (-4) = Y(0) \times I(1)$

   • At $i = 2$: $Y(2) = -800 = (-80) \times 10 = Y(1) \times I(2)$

   • At $i = 3$: $Y(3) = -12000 = (-800) \times 15 = Y(2) \times I(3)$

   Thus, the recurrence relation for $Y(i)$ is:

   $$Y(i) = Y(i - 1)I(i), \quad i > 0$$

Therefore, (A) correctly describes the given data.