In rapidly dividing cells (e.g., E. coli), the completion of the cell cycle is about 20 minutes. Bacterial growth is an increase in cellular constituents and results in an increase in cell size, cell number, or both. When microorganisms are grown in a batch culture, the resulting growth curve usually has four phases. In the exponential phase, the population number of cells undergoing binary fission doubles at a constant interval called the "generation or doubling time".
The mathematics of bacterial growth at the exponential growth phase can be formulated as follows:
[if N0 = the initial population number; Nt = the population at time t; n = the number of generations in time t; doubling time g; growth rate k; the mathematical relation is Nt = N0 x 2^n; k = log(Nt) - log(N0)/log(2t); log2 = 0.3].
In the exponential growth phase, if a bacterial population was increased from 10^4 cells to 10^12 cells in 10 hours,
[Show your calculation for the 3 questions]
a. What is the "doubling time (g)"?
b. What is the growth rate (k) (i.e., how many times divide per hour?)
c. Given an exponential bacterial culture with 1 x 10^6 cells per ml and a generation time of 30 minutes (0.5 hour), how long does it take the culture to reach a density of 6.4 x 10^7 cells per ml?