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

Answer:

21 minutes or 0.35 hours

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 -

$A = 100 * e^{2 * \frac{20}{60} }\\\\A = 195$

Generation time

$G = \frac{t}{3.3 * log \frac{194}{100} } \\G = \frac{t}{0.949} \\G= 21$ minutes

or 0.35 hours