Question

You start off with 100 E. coli cells known to divide every 20 minutes. Based on this information and using formulas for exponential growth (Nt = No2n), 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.

Answer 1

21 minutes or 0.35 hours

Step-by-step explanation:

The formula for exponential population growth is

`A = A_0* e^(kt)\\`

where

`A_0 =` initial population of E.coli i.e 100

k is the rate of population growth i.e 2 as the population doubles

t is the time period i.e 20 minutes

Substituting the given values in above equation, we get -

`A = 100 * e^{2 * (20)/(60) }\\\\A = 195`

Generation time

`G = (t)/(3.3 * log (194)/(100) ) \\G = (t)/(0.949) \\G= 21` minutes

or 0.35 hours