In a city, the construction of new establishments (E(t)) depends on the number of people (N(t)) living there. In addition, the number of people in the city increases, due to migration from nearby towns, at a rate depending on the establishments that are available for the people in the city. Setup differential equation(s) for the number of establishments (E(t)) and the number of people in the city (N()), solve them to find how each of them grows in time? Assume - there were no people in the city when there were no establishments. In addition, state some of the limitations of this simple model of a city.
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