Question

At 4:00 p.m. a closed flask of sterile broth is inoculated with 10,000 cells. The lag phase lasts 1 hour. At 9:00 p.m. the log phase culture has a population of 65 million cells. The mean generation time is approximately

• 10 minutes.

• 40 minutes.

• 20 minutes.

• 30 minutes.

The correct answer is 20 minutes, but can you please show me how to get to this answer?

Answer 1

The answer to your query is as follows:

Under favorable conditions in the laboratory, the bacterial population is doubled at regular intervals and the growth is done in the form of geometric progression. It is like 1, 2, 4, 8, ......2n. This form of growth is called exponential growth where n = the number of generations of the bacterial population.

The generation time can be defined as the rate of the exponential growth of a bacterial culture by binary fission. It can also be called as the doubling time of the bacterial population.

Generation time (G) = time (t)/number of generation (n)

G = t/n

t = time (hours or minutes)

B = number of bacterial cells at the starting of a time interval t

b = number of bacterial cells at the end of the time interval t

n = number of generations or number of times the bacterial cell population is doubled

b = B x 2n (Expression of bacterial growth by binary fission)

Solving for n:

logb = logB + nlog2

n = logb - logB

  log2

n = logb - logB

  .301

n = 3.3 logb/B

G = t/n

Solving for G

G =    t

  3.3 log b/B

According to the question, the conditions are as follows:

B= 10,000

b = 65,000,000

t = 240 min (4 hours from 5:00 p.m. to 9:00 p.m.)

Though the experiment started at 4:00 p.m., in which a closed flask of sterile broth was inoculated with 10,000 cells but there was a lag phase that lasted for 1 hour. Thus, to calculate the generation time in the exponential phase we will remove the 1 hour of lag phase from the total time of the experiment.

Substituting all the values in the given formula,

Solving for G

G =    t

  3.3 log b/B

G =    240

  3.3 log 65,000,000/10,000

G =    240

  3.3 x 3.81

G= 20 minutes (approx)

Hope it helps!