A) If a culture of bacteria starts with 23 cells and the population grows expone
ID: 165276 • Letter: A
Question
A) If a culture of bacteria starts with 23 cells and the population grows exponentially, how many cells will there be after 16 generations?
B) At a certain time during the exponential phase of a bacterial growth experiment, the absorbance of the culture is 0.5 AU.
Exactly 70 minutes later, the absorbance is 2.3 AU.
Assuming the culture is still in the log phase, what is the generation time?
The units for your answer should be in minutes, but do not enter the units in your numerical response.
(Hint: the log of 2.3 = 0.361725494195737, and the log of 0.5 = -0.301)
C)You have determined the generation time of a bacterial culture to be 20 minutes in log phase.
What is the growth rate constant?
Explanation / Answer
Answers:
A) Total number of cells in an exponentially growing bacterial culture can be calculated using following formula:
Total number of cells = 2n x number of initial cells
Where, n is number of generations.
Thus, starting with 23 initial cells, after 16 generations, total number of cells in the culture will be 1,507,328. See below:
Total number of cells = 216 x 23 = 1,507,328 cells
B) For calculating generation time, you first need to calculate number of generations. Following formula can be used to calculate the number of generations:
No. of generations = log of cells at the end of incubation - log of cells at the begning of incubation / log 2
Thus, for the above case,
No. of generations = log 2.3 - log 0.5 / log 2
No. of generations = 0.361 - (-0.301) / 0.301
No. of generations = 2.199
Now the generation time can be calculated as follows:
Generation time (in minutes) = incubation time in minute / no. of generations
Thus, Generation time = 70/2.199 = 31.8
Generation time = ~ 32 minutes per generation
C) During logarithmic growth phase bacterial cultures mimic the first order chemical reaction, means the rate of increase of cells is proportional to the number of bacterial cells present at that perticular time. The constant of this proportionality is called as growth rate constant 'K'. This exponential growth rate constant is reciprocal to the generation time. Thus, growth rate constant value can be calculated as follows:
Generation time (in hours) = 1/K
20/60 = 1/K
1/3 = 1/K
Thus, growth rate constant, K = 3 doublings per hour.