Evaluate \(y=0.5x+7\) at \(x=20\) after fitting the model on \(10\le~x\le~15\). Calculate \(y\), classify the use as interpolation or extrapolation, and state the extension caveat.

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The model gives y=17; this is an extrapolation, so 17 depends on extending the fitted relationship.

The model gives y=27; this is an extrapolation, so 27 depends on extending the fitted relationship.

The model gives y=17; this is an interpolation, so 17 is guaranteed by observed data.

The model gives y=17; this is an extrapolation, so 17 is an exact observed value.

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Curriculum context

Course: Math I
Standard: S-ID.6.c
Category: Statistics and Probability
Domain: Interpreting Categorical and Quantitative Data
Objective: Fit a linear function to data when a scatter plot suggests a linear association.
Problem type: Use a linear model to extrapolate cautiously