Problem

Analyze the displayed table using first differences, second differences, and ratios. Classify the pattern, determine its exact model, and state the decisive evidence.

Raw source data or graph without classification cues.

Big Picture

What this problem is really about

Failing one pattern test does not finish the classification, because the data may belong to another family. With equal input steps confirmed, we’ll compute first differences and ratios, then examine second differences if neither stays constant. Recognizing the output pattern itself can turn that family evidence into an exact rule.

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first differences = 3,5,7, not constant; second differences = 2,2, constant; ratios = 4,9/4,16/9, not constant; family = exponential; model = y=4ˣ; evidence = first ratio is 4

first differences = 3,5,7, not constant; second differences = 2,2, constant; ratios = 4,9/4,16/9, not constant; family = quadratic; model = y=(x+1)²; evidence = constant second differences

first differences = 3,5,7, not constant; second differences = 2,2, constant; ratios = 4,9/4,16/9, not constant; family = linear; model = y=3x+1; evidence = first difference begins at 3

first differences = 3,5,7, not constant; second differences = 2,2, constant; ratios = 4,9/4,16/9, not constant; family = neither; model = none; evidence = first differences are not constant

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Analyze the displayed table using first differences, second differences, and ratios. Classify the pattern, determine its exact model, and state the decisive evidence.

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