Question

Consider a culture of E. coli growing in exponential phase with a generation time of 20 minutes. Beginning with 2 x 10⁶ cells per ml, how long will it take the culture to reach a density of about 3.2 x 10⁷ cells per ml?

Answer 1

Question: Consider a culture of E. coli growing in exponential phase with a generation time of 20 minutes. Beginning with 2 x 10⁶ cells per ml, how long will it take the culture to reach a density of about 3.2 x 10⁷ cells per ml?

Answer: t = 80 min

We know that, G (generation time) = t/n ---(1)

G = generation time

t = time interval in hours or minutes

n = number of generations

Given that;

Generation time = 20 minutes

N₀ = number of bacteria at the beginning of a time interval = 2 x 10⁶ cells per ml

N = number of bacteria at the end of the time interval =  3.2 x 10⁷ cells per ml

N = N₀ x 2ⁿ ---(2)

Solve for n:

logN = logN₀ + n log2

n = (logN - logN₀) / log2

n =  (logN - logN₀) / 0.301 log2 = 0.301   

n = 3.3 log N/N₀

Using eqtn(1), t = Gn

t = (20 minutes) {3.3 x log (3.2 x 10⁷ cells per ml / 2 x 10⁶ cells per ml)}

= (20) {3.3 x log 16} = 79.47 min ~ 80 min