Analyze the displayed table to determine the function family and model, support the result with difference and ratio evidence including any relevant output shift, and state the assumption required for long-term use.

Accelerating differences can signal an exponential structure even when the raw outputs do not have a constant ratio. We’ll calculate the first differences, notice how those changes scale, and test a vertical shift that exposes repeated multiplication. Building the rule from the shifted values will also make clear what continuation assumption is required beyond the observed inputs.