Construct linear and exponential functions, including arithmetic/geometric sequences, from graphs, descriptions, or input-output pairs.
Decide whether to construct a linear or exponential model from table values
Problem
Use the displayed raw value table. Decide whether a linear or exponential model is more appropriate and identify the constant-difference or constant-ratio evidence.
Increasing outputs are not automatically exponential; the kind of repeated change is what identifies the model family. With equally spaced inputs, we’ll calculate every consecutive difference and compare the corresponding ratios. A stable additive change supports a linear structure, while the ratio check guards against mistaking ordinary growth for exponential growth.
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