Use the displayed table, representative factor \(1.10\), and \(\text{residual}~=~\text{observed}~-~\text{predicted}\) to evaluate an exponential fit. Calculate the ratios, model and percent change, predictions and residuals, then state whether the fit is exact or approximate.

Real data can support an exponential model even when its ratios are close rather than identical. We’ll compare consecutive outputs over equal input steps, use a representative factor to build the model, and keep predicted values separate from observations. Signed residuals will then show both how well the model fits and why a small miss makes the fit approximate instead of exact.