infeced pool

Algebra Level pending

I built a new pool in my backyard. Accidentally I left free a substance with a dangerous virus that reproduces itself in the next way: The first day the pool had a total of 1 cubic centimeter of the virus. The second day the pool had a total of 2 cubic centimeters of the virus. The third day the pool had total of 4 cubic centimeters of the virus. And it continued reproducing with the same ratio for a long time. Then I realised that my pool was completely filled with the virus at the day 48. In which day did my pool was half filled with the virus?

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