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M1-031-A13-V02
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F-LE.2
Warmup
M1-031-A13-V02
Construct linear and exponential functions, including arithmetic/geometric sequences, from graphs, descriptions, or input-output pairs.
Construct a model and use it to predict
Problem
Use the displayed data to determine and verify a model, predict \(f(8)\), classify the prediction as interpolation or extrapolation, and state the continuation assumption.
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A
model = f(x)=5x+50 from differences 5; verification = f(0)=50,f(1)=55,f(2)=60; prediction = f(8)=85; type = extrapolation; assumption = constant +5 change continues
B
model = f(x)=50x+5 from differences 50; verification = f(0)=5,f(1)=55,f(2)=105; prediction = f(8)=405; type = extrapolation; assumption = constant +50 change continues
C
model = f(x)=5x+50 from differences 5; verification = f(0)=50,f(1)=55,f(2)=60; prediction = f(8)=90; type = extrapolation beyond [0,2]; assumption = constant +5 change continues
D
model = f(x)=5x+50 from differences 5; verification = f(0)=50,f(1)=55,f(2)=60; prediction = f(8)=90; type = interpolation because 8 is whole; assumption = constant +5 change continues
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Curriculum context
Standard F-LE.2
Category Functions
Domain Linear, Quadratic, and Exponential Models
Objective Construct linear and exponential functions, including arithmetic/geometric sequences, from graphs, descriptions, or input-output pairs.
Problem type Construct a model and use it to predict
