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M1-028-A09-V02
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F-LE.1.a
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M1-028-A09-V02
Distinguish linear from exponential situations by equal differences versus equal factors over equal intervals.
Show data is neither linear nor exponential
Problem
Analyze the displayed table using differences, ratios, and any relevant shift of the outputs. Classify the pattern, determine its exact model, and state the decisive evidence.
Answer choices
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A
raw differences = 3,6,12, not constant; raw ratios = 5/2,11/5,23/11, not constant; shifted outputs y+1 = 3,6,12,24 have ratio 2; family = quadratic; model = y=x²+2; evidence = differences increase
B
raw differences = 3,6,12, not constant; raw ratios = 5/2,11/5,23/11, not constant; shifted outputs y+1 = 3,6,12,24 have ratio 2; family = shifted exponential; model = y=3·2ˣ-1; evidence = constant shifted ratio
C
raw differences = 3,6,12, not constant; raw ratios = 5/2,11/5,23/11, not constant; shifted outputs y+1 = 3,6,12,24 have ratio 2; family = shifted exponential; model = y=2·3ˣ-1; evidence = coefficient and base can swap
D
raw differences = 3,6,12, not constant; raw ratios = 5/2,11/5,23/11, not constant; shifted outputs y+1 = 3,6,12,24 have ratio 2; family = neither; model = none; evidence = raw ratios are not constant
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Curriculum context
Standard F-LE.1.a
Category Functions
Domain Linear, Quadratic, and Exponential Models
Objective Distinguish linear from exponential situations by equal differences versus equal factors over equal intervals.
Problem type Show data is neither linear nor exponential
