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A colony of bacteria is a container grows by each bacterium splitting into eight next generation bacteria. However, because of environmental conditions, only $50$% of the bacteria in a generation can split as above. A colony of first generation bacteria was put in the container and it was found that the number of seventh generation bacteria was $4096$ million. What was the size of the first generation population initially put in the container?

  1. $2$ million
  2. $8$ million
  3. $1$ million
  4. $4$ million
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