Which one of the following options is correct for the given data in the table?…
2025
Which one of the following options is correct for the given data in the table?
\(\begin{array}{|c|c|c|c|c|} \hline \text{Iteration (i)} & \text{0} & \text{1} & \text{2} & \text{3} \\ \hline \text{Input (I)} & \text{20} & \text{-4} & \text{10} & \text{15} \\ \hline \text{Output (X)} & \text{20} & \text{16} & \text{26} & \text{41} \\ \hline \text{Output (Y)} & \text{20} & \text{-80} & \text{-800} & \text{-12000} \\ \hline \end{array}\)
- A.
\(𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖 > 0\) - B.
\(𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1) + 𝐼(𝑖); 𝑖 > 0\) - C.
\(𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖 > 0\) - D.
\(𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖 − 1); 𝑖 > 0\)
Attempted by 14 students.
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Correct answer: A
Solution overview: find the recurrences that reproduce the table of values.
Determine how each output changes from one iteration to the next:
X recurrence: X(i) = X(i-1) + I(i)
i = 1: X1 = 20 + (-4) = 16
i = 2: X2 = 16 + 10 = 26
i = 3: X3 = 26 + 15 = 41
Y recurrence: Y(i) = Y(i-1) × I(i)
i = 1: Y1 = 20 × (-4) = -80
i = 2: Y2 = -80 × 10 = -800
i = 3: Y3 = -800 × 15 = -12000
Conclusion: The recurrences that match every row of the table are X(i) = X(i-1) + I(i) and Y(i) = Y(i-1) × I(i) for i > 0.
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