Problem

For \(x=0,1,2,3,4\) and \(y=2,4,8,16,32\), calculate first differences and successive ratios, determine whether linear or exponential form is appropriate, and state the evidence.

Source modeling plot: For x=0,1,2,3,4, data y=2,4,8,16,32, assess exponential versus linear form. No fitted model or assessment is annotated.

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differences=2,4,8,16 not constant; ratios=2,2,2,2; selected=another nonlinear family; evidence=nonlinearity is treated as requiring a model other than exponential

differences=2,4,8,16 not constant; ratios=2,2,2,2; selected=not exponential because differences are unequal; evidence=additive differences are treated as the exponential criterion

differences=2,4,8,16 not constant; ratios=2,2,2,2; selected=linear because values increase; evidence=increasing output is treated as linear evidence

differences=2,4,8,16 not constant; ratios=2,2,2,2; selected=exponential growth; evidence=constant multiplicative factor2 for equal x-steps

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For \(x=0,1,2,3,4\) and \(y=2,4,8,16,32\), calculate first differences and successive ratios, determine whether linear or exponential form is appropriate, and state the evidence.

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