Question

Starting with 10 bacterial cells per milliliter in a sufficient amount of complete culture medium with a 1 hour lag phase and a 30-min generation time, how many cells will be in the liter of medium at the end of 2 hours? At the end of 7 hours?

i need an explanation of each step.

Answer 1

The lag phase is the phase where the bacteria prepares itself for cell division. During this phase, no actual cell division occurs. After the lag phase ends, the log phase begins when there is an exponential increase in the number of bacteria cells.

Generation time is the time required by bacteria to double itself in number. Thus, it is also called doubling time (D)

Here, the generation time (D) is 30 minutes = 0.5 hours

Initial number of bacteria (N_o) = 10 bacterial cells per mililiter

Let the time during which exponential growth occurs be t

At the end of 2 hours:

In the first 1 hour there will be no growth due to lag phase.

In the next 1 hour, there will be exponential growth.

Thus, t = 1 hour

Number of bacteria at the end = Initial number of bacteria x (2)^t/D

= 10 x (2)^1/0.5

= 10 x (2)²

= 10 x 4 = 40 bacterial cells per mililiter

At the end of 7 hours:

In the first 1 hour there will be no growth due to lag phase.

In the next 6 hour, there will be exponential growth.

Thus, t = 6 hour

Number of bacteria at the end = Initial number of bacteria x (2)^t/D

= 10 x (2)^6/0.5

= 10 x (2)¹²

= 10 x 4096 = 40960 bacterial cells per mililiter

______________________________________

[Kindly give a thumbs up]