Problem

Use the displayed table, representative factor \(0.90\), 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, 500), (1, 449), (2, 405), and (3, 365).

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ratios = 0.898,405/449≈0.9020,365/405≈0.9012; model = f(x)=500·0.10ˣ; rate = 90% decay/interval; predictions = 500,50,5,0.5; residuals = 0,399,400,364.5; conclusion = poor exponential fit using factor 0.10

ratios = 0.898,405/449≈0.9020,365/405≈0.9012; model = f(x)=500·0.90ˣ; rate = 10% decay/interval; predictions = 500,450,405,364.5; residuals = 0,1,0,-0.5; conclusion = good approximate fit using predicted-minus-observed residuals

ratios = 0.898,405/449≈0.9020,365/405≈0.9012; model = f(x)=500·0.90ˣ; rate = about 10% decay/interval; predictions = 500,450,405,364.5; residuals = 0,-1,0,0.5; conclusion = good approximate exponential fit with deviations at x=1 and x=3

ratios = 0.898,405/449≈0.9020,365/405≈0.9012; model = f(x)=500·0.90ˣ; rate = 90% decay/interval; predictions = 500,450,405,364.5; residuals = 0,-1,0,0.5; conclusion = good approximate exponential fit

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Use the displayed table, representative factor \(0.90\), 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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