A high$-$tech manufacturing facility installs a specialized production machine with an initial cost of $$12,000,000.$ The machine has an estimated total production capacity of $10,000,000$ units. In the first year, the machine produces $1,200,000$ units. However, due to increasing demand, the production rate in subsequent years increase by $20\%$ annually. Calculate the depreciation using the units of production method for the first three years, considering the changing production rates.