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A simple electric motor has an armature resistance of 1Omega and runs from a dc source of 12 volt . When running unloaded it draws a current of 2 amp . When a certain load is connected , its speed becomes one-half of its unloaded value . The new value of current drawn

Anthropologists determine that new dwellings in an ancient farming community were constructed monthly as modeled by the function f(x)=2x+100, where x is the current month of the year and f(x) is the number of dwellings constructed by the end of that month. Additionally, they determine that the population grew exponentially each month, thanks to the discovery of more fertile land for farming. This growth is modeled by the equation g(x)=3^x , where g(x) represents the current population at the end of a given month. What is the smallest integer value of x, with 1 representing the end of January and 12 representing the end of December, at which the population surpasses the number of dwellings built?