The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 30 min.
(b) How long would it take for a colony of 50 cells to increase to a population of 1 million? (Round your answer to the nearest whole number.)
To find out how long it would take for a colony of 50 cells to increase to a population of 1 million, we need to determine how many times the population doubles.
Start by understanding that the growth rate of Escherichia coli is proportional to its size and that it doubles approximately every 30 minutes.
To calculate the number of times the population doubles, divide the final population (1 million) by the initial population (50):
1,000,000 / 50 = 20,000
So, the population needs to double 20,000 times to reach 1 million cells.
Since each doubling takes approximately 30 minutes, multiply the number of doublings by the time per doubling:
20,000 * 30 minutes = 600,000 minutes
Now, to round your answer to the nearest whole number, divide the total minutes by 60 (the number of minutes in an hour):
600,000 minutes / 60 minutes = 10,000 hours
Therefore, it would take approximately 10,000 hours for the colony of 50 cells to increase to a population of 1 million.