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M1-028-A10-V04
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F-LE.1.a
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M1-028-A10-V04
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 = -40,-32,-25.6, not constant; ratios = 0.80,0.80,0.80, constant; family = exponential; model = A(m)=200·0.80ᵐ; change = retains 20% and decays 80%/month; reject linear = changes are multiplicative
B
differences = -40,-32,-25.6, not constant; ratios = 0.80,0.80,0.80, constant; family = exponential; model = A(m)=200·0.20ᵐ; change = retains 20% and decays 80%/month; reject linear = changes are multiplicative
C
differences = -40,-32,-25.6, not constant; ratios = 0.80,0.80,0.80, constant; family = linear; model = A(m)=200-40m; change = -40 units/month; reject exponential = decreasing values are linear
D
differences = -40,-32,-25.6, not constant; ratios = 0.80,0.80,0.80, constant; family = exponential; model = A(m)=200·0.80ᵐ; change = retains 80% and decays 20%/month; reject linear = decreases 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
