Distinguish additive change from multiplicative change in tables, graphs, and contexts.
Compare two growth patterns
Problem
Table A maps \(x~=~1,~2,~3,~4\) to \(y~=~7,~12,~17,~22\). Table B maps \(x~=~1,~2,~3,~4\) to \(y~=~3,~6,~12,~24\). Compare their consecutive differences and factors, then classify each table as additive or multiplicative.
Analyze the tables independently even though they share the same inputs. For each output column, compute all adjacent differences; if those are not constant, compare adjacent ratios instead. One table’s behavior cannot determine the other’s classification, so require a repeated amount or repeated factor across every row transition before assigning either type.
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