On earth, a certain type of bacteria doubles in number every 24 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture is left on earth and the other is put on a rocket travelling at .866c relative to the earth. By the time the earth bound bacteria have grown to 256 bacteria, how many bacteria are in the culture on the rocket, according to earth-based observers?

Answer 1

Time on the rocket goes more slowly, as seen by earth-based observer. The elapsed time on the rocket is lower by a factor sqrt[1-(v/c)^2] = sqrt(0.25) = 1/2

2^8 = 256 is the number of bacteria that are produced on earth during the time interval you are discussing.

The rocket's bacteria will have doubled half as many times, so there will be 2^4 = 16 bacteria