Calculating Growth Rate of Bacteria

 
How to calculate growth rate:

During balanced growth, the growth mimics a first order chemical reaction.
dN/dt =kN
N is the concentration of cells, t the time and k is the growth rate constant.
The dimension of the specific growth rate k are reciprocal time, usually expressed as reciprocal hours, or hr^1.
Integration of previous equation between the limits of 0 and t and N1 and N2 gives following equation.
ln(N2/N1)=k(t2-t1)
converting the previous equation to logarithmns to the base of 10, we get
log10N2-log10N1 = k(t2-t1)/2.303
If one determines the number of bacterial CFUs present at various times and plots the log of that number, one gets a straight line (in log phase)
From the slope of the line, we can calculate the specific growth rate k of the culture, which is the most encompassing parameter of how fast a
particular bacterium growths in a particular media. For example, if a culture contains 10^3 cells at time t1 and 10^8 cells at t2 6 hours later,
the specific growth rate k is
k= (8-3) 2.303/6, which equals k=1.92 hr^-1
The dimension of the specific growth rate k are reciprocal time, usually expressed as reciprocal hours, or hr^1.
How to calculate Generation or Doubling time:
The rate of growth of a bacterial culture is oftern described by the time required for the number of cells to increase by a factor of 2, or the
DOUBLING TIME or GENERATION TIME, g.
The relationship between g and k can be established by using following equation.
ln(N2/N1)=k(t2-t1)
ln is the natural logs (log^e)
N2 is cell number at t2 and N1 is the cell number at t1
k is the growth rate
Since when N2 = 2N1, t2-t1 becomes equal to g
Substituting values for t and N into the previous equation, we obtain following:
g=ln2/k = 0.693k
(reference: Physiology of the bacterial cell, a molecular approach by Frederick C. Neidhardt, John Ingraham and Moselio Schaechter)