Distinguish additive change from multiplicative change in tables, graphs, and contexts.
Model a story with a table and classify it
Problem
A game show contestant has \(7~\text{points}\) after round \(1\) and gains \(7~\text{points}\) each new round. Generate the complete round-total table for rounds \(1~\text{through}~4\) and classify the change as additive or multiplicative.
Big Picture
What this problem is really about
Build the table from the story in chronological order: enter the stated total after round one, then apply the same gain to each newest total for the next round. Once all four rows are present, compare consecutive totals to verify that the change is constant. The operation used between rows—not merely the fact that scores rise—determines the classification.
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