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M1-028-A10-V02
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F-LE.1.a
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M1-028-A10-V02
Distinguish linear from exponential situations by equal differences versus equal factors over equal intervals.
Choose a linear or exponential model from data evidence
Problem
Analyze the displayed time-value table by comparing consecutive differences and ratios. Determine the model family and exact model, state the rate or percent change, and explain why the other family is inappropriate.
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A
differences = 7,7,7, constant; ratios = 27/20,34/27,41/34, not constant; family = linear; model = A(w)=20+7w; change = +7 units/week; reject exponential = ratios are not constant
B
differences = 7,7,7, constant; ratios = 27/20,34/27,41/34, not constant; family = exponential; model = A(w)=20·1.35ʷ; change = 35% growth/week; reject linear = outputs increase
C
differences = 7,7,7, constant; ratios = 27/20,34/27,41/34, not constant; family = exponential; model = A(w)=20·1.35ʷ; change = first ratio 1.35; reject linear = first ratio determines all ratios
D
differences = 7,7,7, constant; ratios = 27/20,34/27,41/34, not constant; family = linear; model = A(w)=7+20w; change = +20 units/week; reject exponential = 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 Choose a linear or exponential model from data evidence
