Question

1. You start off with 100 E. coli cells known to divide every 20 minutes. Based on this information and using formulas for exponential growth (N_t = N_o2ⁿ), growth constant (k = n/t (gen/hr), and generation time (g = t/n or 1/g (hr/gen), calculate the following:   

a.      From the given information, what is the generation time? Remember it’s the length of time (in hours) for the population to double.

b.      How many bacteria will be present after 3 hours?

c.      What is the growth constant for these bacteria?

2. Mycobacteria are notoriously slow to grow. Some species can take 12 hours to divide and double in population size. Suppose you take a sputum sample for a patient and grow the bacteria in broth for 10 days. At the end of the 10 days, you perform standard plate count (via serial dilution and plating) and discover that a total of 4.20 x 10⁶ mycobacteria are present.  

1. What is the generation time for this bacterium?
2. How many generations have passed during the 10 days period?
3. Calculate the initial number of bacteria that were inoculated into the broth.  
4. Calculate the growth rate for this bacterium.

Answer 1

1) a) given that it takes 20 minutes to divide

1 hour=60 minute, then 1 minute is 1/60 hours

so 20 minutes= 20/60=1/3 hours

b) 3 hours=360= 180 minutes

then number of generations= time/generation time

= 180/20

= 9

N_t = N_o2ⁿ

Nt=number of cells after time t, N0= number of cells present initially=100, n= number of generations=9

Nt=100 2^9

= 51200 cells

number of cells after 3 hours= 51200

c) growth constant k= n/t

n= number of generations, t=time taken to grow

in 3 hours there were 9 generations so

growth constant= 9/3= 3 generations/ hour