Problem

Use the displayed table, representative factor \(1.30\), 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.

Table of observed points (0, 50), (1, 65), (2, 85), and (3, 110).

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ratios = 1.30,85/65≈1.3077,110/85≈1.2941; model = f(x)=50·1.30ˣ; rate = 30% growth/interval; predictions = 50,65,85,110; residuals = 0,0,0,0; conclusion = exact fit because observed values are used as predictions

ratios = 1.30,85/65≈1.3077,110/85≈1.2941; model = f(x)=50+15x; rate = 15 units/interval; predictions = 50,65,80,95; residuals = 0,0,5,15; conclusion = good linear fit because the first increase repeats

ratios = 1.30,85/65≈1.3077,110/85≈1.2941; model = f(x)=50·1.30ˣ; rate = 130% growth/interval; predictions = 50,65,84.5,109.85; residuals = 0,0,0.5,0.15; conclusion = good approximate exponential fit

ratios = 1.30,85/65≈1.3077,110/85≈1.2941; model = f(x)=50·1.30ˣ; rate = about 30% growth/interval; predictions = 50,65,84.5,109.85; residuals = 0,0,0.5,0.15; conclusion = good approximate exponential fit, not exact at later inputs

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Use the displayed table, representative factor \(1.30\), 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.

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