Question

A 100 μl sample containing 1000 bacterial cells/μl in log phase growth is added to 9.9 ml of fresh culture medium broth. Assuming no nutrients are in limited supply, and a generation time of 30 minutes, how many bacteria will be present in the entire broth culture after six hours? ______

A) 6.0 × 106
B) 2.56 × 107
C) 1.2 × 106
D) 4.096 × 108
E) 6.0 × 105

Answer 1

The number of bacteria present in the entire broth culture after six hours, with an initial population of 1000 cells/μl and a generation time of 30 minutes, is 4.096 x 10^8 cells, corresponding to answer choice D) 4.096 x 10^8.

Step-by-step explanation:

To calculate the number of bacteria present in the entire broth culture after six hours, we'll use the formula for exponential growth, which is N = N0 x 2^n, where N is the final population size, N0 is the initial population size, and n is the number of generations. First, we need to determine the number of generations that occur in six hours. With a generation time of 30 minutes, there would be 12 generations in six hours (6 hours * 2 generations per hour).

Next, we calculate the initial population size in the 9.9 mL of broth. Since 100 μl (0.1 mL) of the original culture was added to 9.9 mL of broth, the starting concentration would be 1000 cells/μl. Therefore, the initial population, N0, is 1000 cells/μl * 100 μl = 100,000 cells.

Now we apply the exponential growth formula. We get N = 100,000 cells * 2^12 = 100,000 cells * 4096 = 409,600,000 cells. In scientific notation, this is 4.096 x 10^8 cells.