I built a new model for this exercise but kept the immigration and emigration graphical functions from the last exercise because they don't relate in any obvious way to time or prosperity. I modeled per capita GDP as a function of time: GDP = 1.826*e ^ (.02*t) where t = year with 1851 = 0. I developed that equation from a quick web search for historical economic data. I then modeled natality and mortality as functions of per capita income: natality = 0.0507*GDP^-0.34 and mortality = 0.0268*GDP^-0.377. Here is the result:

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