Problem

Analyze the displayed time-value table by comparing consecutive differences and ratios. Determine the model family and exact model, state the rate or percent change, and explain why the other family is inappropriate.

Table with year t values 0, 1, 2, 3 and account A(t) values 100, 110, 121, 133.1.

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What this problem is really about

Equal time steps let us put additive and multiplicative evidence side by side. We’ll calculate every consecutive difference and ratio, identify which pattern remains constant, and combine that pattern with the initial value to build a model. Finally, we’ll translate any multiplicative factor into a percent change without confusing the retained amount with the increase itself.

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differences = 10,11,12.1, not constant; ratios = 1.10,1.10,1.10, constant; family = exponential; model = A(t)=100·0.10ᵗ; change = retains 10%/year; reject linear = changes are multiplicative

differences = 10,11,12.1, approximately 10; ratios = 1.10,1.10,1.10; family = linear; model = A(t)=100+10t; change = 10 units/year; reject exponential = ratios do not matter

differences = 10,11,12.1, not constant; ratios = 1.10,1.10,1.10, constant; family = exponential; model = A(t)=100·1.10ᵗ; change = 110% growth/year; reject linear = changes are multiplicative

differences = 10,11,12.1, not constant; ratios = 1.10,1.10,1.10, constant; family = exponential; model = A(t)=100·1.10ᵗ; change = 10% growth/year; reject linear = dollar increases are not constant

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Analyze the displayed time-value table by comparing consecutive differences and ratios. Determine the model family and exact model, state the rate or percent change, and explain why the other family is inappropriate.

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