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 linear model through \((0,~10)\) and \((2,~18)\) to determine and verify its equation, predict \(f(5)\), classify the prediction as interpolation or extrapolation, and state the continuation assumption.
Big Picture
What this problem is really about
A prediction is only as sound as both its fitted model and the assumption used to extend that model. We’ll derive the line from the observed points, verify it at those inputs, and then evaluate it at the requested input. Comparing that input with the observed interval will distinguish interpolation from extrapolation and expose the continuation assumption behind the prediction.
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