Question

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

• A. \quad X(i) = X(i - 1) + I(i); \quad Y(i) = Y(i - 1) I(i); \quad i%gt;0
• B. \quad X(i) = X(i - 1) I(i); \quad Y(i) = Y(i - 1) + I(i); \quad i%gt;0
• C. \quad X(i) = X(i - 1) I(i); \quad Y(i) = Y(i - 1) I(i); \quad i%gt;0
• D. \quad X(i) = X(i - 1) + I(i); \quad Y(i) = Y(i - 1) I(i - 1); \quad i%gt;0

Hint:

For numerical pattern recognition problems, systematically verify each given option using sample values from the table. Identifying trends in addition, multiplication, or other operations can help derive the correct recurrence relations.

Answer 1

The Correct Option is A

Observing the pattern in the given table: For \(X(i)\): \[ X(1) = X(0) + I(1) = 20 + (-4) = 16 \] \[ X(2) = X(1) + I(2) = 16 + 10 = 26 \] \[ X(3) = X(2) + I(3) = 26 + 15 = 41 \] For \(Y(i)\): \[ Y(1) = Y(0) \times I(1) = 20 \times (-4) = -80 \] \[ Y(2) = Y(1) \times I(2) = (-80) \times 10 = -800 \] \[ Y(3) = Y(2) \times I(3) = (-800) \times 15 = -12000 \] Since the calculations match the given table, the correct option is (A).