As viewed on earth, a certain kind of bacteria is recognized to double in number each and every 27.3 hour. The two cultures of these bacteria are prepared, each comprising primarily of one bacterium. One culture is left on earth and the other positioned on a rocket which travels at a speed of 0.787c relative to the earth. At a time when the earthbound culture has grown to 32 bacteria, determine how many bacteria are in the culture on the rocket, according to the earth-based observer?