Question

3. A culture medium was inoculated with 1200 cells and incubated for 4 hours. At the end of incubation there were 106,000 cells. Calculate the generation time and growth rate of the culture. Show your work to get full credit. (5pts)

Answer 1

Bacterial cells divide by binary fission. Time taken to get divided into two cells is called generation time. It is a geometric expression. When there is one cell in the beginning, it will be 2 at the end of the first generation and will become 4 at the end of the second generation. So it goes like 2⁰, 2¹, 2²,... 2ⁿ.

Generation time G= t/n,

where t = time interval in hours or minutes

n = number of generations

In the above question number of generation is not given.

So, to find the number of generation,

n= logb - logB/log2

where B =number of bacteria at the beginning of the time interval

b = number of bacteria at the end of the time interval

Substitute all the values

n = log (106000) - log (1200)/ log2 = 5.025 - 3.079 / 0.301 = 1.945/0.301 = 6.46

Number of generation n = 6.46

generation time G = 4/ 6.46 = 0.619 hours = 37 minutes

Growth rate N_t = N₀ X (1+r)^t

Where, N_{t =} amount at time t

N₀ = Amount at time zero

r = growth rate

106000 = 1200 X (1+r)⁴ ; (1+r)⁴ = 106000/ 1200 ; (1+r)⁴ = 88.33; (1+r) = (88.33)^1/4 ; (1+r) = 3.04; r = 3.04 -1 = 2.04