A stationary phase of Ecoli grown in rich medium contains 10

A stationary phase of E.coli grown in rich medium contains ~10^9 CFU/ml and a typical growth curve is inoculated with ~10^6 CFU/ml. Given a typical Hebron
generation time for bacterium in favorable growth conditions is about 20 minutes (growth rate of 3.33 generations per hour), determine about how long it would take the positive control culture to reach stationary phase (in hours).

Solution

Given data:

Starting concentration S = 10⁶ CFU/ml

Final statioinary concentration F = 10⁹ CFU/ml

Generation time (time in doubling) = 20 minutes

Now, calculate the number of generations (n) traversed in arriving from S to F.

2 ⁿ = F/S

2 ⁿ = 10⁹/10⁶

2 ⁿ = 10³

^{Taking Log in both sides}

n log 2 = 3 log 10

n = (3 log 10) / log 2

n = (3 x 1) / 0.3010

Number of generations will be = 9.967

Now, each generation takes 20 minutes to complete. So 9.967 generations will take

9.967 x 20 minutes = 199.34 minutes

OR 199.34 / 60 = 3.32 hours