Final answer:
The length of the doubling period is 4 hours.
Step-by-step explanation:
The bacteria culture starts with 3000 bacteria and after 3 hours, there are 48000 bacteria present. To find the length of the doubling period, we need to determine how many times the population has doubled in those 3 hours. We can do this by calculating the growth factor, which is the ratio of the final population to the initial population. In this case, the growth factor is 48000/3000 = 16.
Since the population doubles with each doubling period, we can calculate the length of the doubling period by taking the log base 2 of the growth factor.
Log base 2 of 16 is equal to 4, so the length of the doubling period is 4 hours.