The following table gives the U.S. national consumption and disposable income (both in billions of dollars) for selected years from 2012 and projected to 2040. Suppose the marginal propensity to consume can be modeled by 

dC/dy = 0.0169y + 0.617

where y equals the disposable income.

(a) Use the data point for 2012 to find the U.S. national consumption function.

(b) Use the data to develop a model of the same function type as found in part (a). Report your model with 3 significant digit coefficients.

(c) Compare your answers to parts (a) and (b). Name one other function type that would be a good model for these data.

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Consump- Consump- Year Income tion Year Income tion 2012 10.2 9.6 2028 17.1 15.4 2014 11.8 10.9 2030 17.8 16.1 2016 12.6 11.6 2032 18.5 16.8 2018 13.5 12.3 2034 19.3 17.5 2020 14.2 12.9 2036 20.1 18.3 2022 14.8 13.4 2038 20.9 19.1 2024 15.5 14.0 2040 21.9 19.9 2026 16.3 14.7