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M1-029-A10-V02
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F-LE.1.b
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M1-029-A10-V02
Recognize constant rate of change as evidence for a linear model.
Diagnose a nonlinear table
Problem
Analyze the displayed table. Test linearity using interval slopes, identify any stronger pattern and exact model the data support, and state the limits of the evidence.
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A
slopes = 3,12,48 over +2 intervals; verdict = not linear because slopes differ; stronger pattern = ratios over +2 inputs are 4,4,4; family = exponential; model = y=2·2ˣ; scope = +2-step ratio 4 gives +1 factor 2
B
slopes = 3,12,48 over +2 intervals; verdict = linear because first slope is 3; stronger pattern = ratios are 4,4,4; family = linear; model = y=3x+2; scope = first interval determines the model
C
slopes = 3,12,48 over +2 intervals; verdict = not linear because slopes differ; stronger pattern = ratios over +2 inputs are 4,4,4; family = exponential; model = y=2·4ˣ; scope = two-step ratio is the one-step factor
D
slopes = 3,12,48 over +2 intervals; verdict = not linear because slopes differ; stronger pattern = ratios are 4,4,4; family = quadratic; model = y=3x²+2; scope = increasing slopes prove quadratic
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Curriculum context
Standard F-LE.1.b
Category Functions
Domain Linear, Quadratic, and Exponential Models
Objective Recognize constant rate of change as evidence for a linear model.
Problem type Diagnose a nonlinear table
