## 2 Bacterial Growth  
The growth of a bacterium is defined as the increase in cells number rather than the cell size. There are certain requirements for bacterial growth and factors that influence the growth process. Temperature, pH, osmotic pressure, mixing, and oxygen concentration are the main factors influencing bacterial growth. There are also nutritional requirements, besides these factors. The replication process is not through mitoses and meiosis, but through a process that is known as binary fission. The DNA of a singular bacterium will be replicated during binary fission (Figure 1). Afterwards, the DNA will be divided, and the cell wall and the membrane will form a transverse septum. The transverse septum will be completely formed, which will enable cells separation, thus generating new bacterial cells. The time interval required for the cell division is one pivotal parameter in bacterial growth, which is known as generation time. The generation time depends on the type of organism and the environmental conditions.  
The bacterial growth consists of four growth phases, which are depicted in Figure 2. In the first phase, the so-called lag phase, the bacteria must physiologically adapt to the culture conditions and growth begins after a period of time. The density in which the cells are distributed is another important factor. Broadly, exoenzymes and nutrients are shared in proximity; however, if the density is low, this could lead to a dilution of these materials [16]. The latter results in slow cell growth and transition to the log phase. Depending on the conditions, the lag phase may take only minutes or several hours. The time length of the lag phase depends on the type of medium.  
The lag phase is followed by the log or exponential phase. In this phase, the cells are in an optimum growth state and they perform binary fission. During the log phase, there is a logarithmic increase in cell number. The slope of this line is the bacterial growth. The mathematical description of the bacterial growth in the log phase can be described while using the following equation:  
\[\frac{\delta N}{\delta t}=\mu N \tag{1}\]  
where \(N\) is defined as the cell number, \(t\) as the time and \(\mu\) as the specific growth rate constant (1/time).  
This leads to the following expression for the number of present cells (exponential growth), which is given by:  
\[N=N_{0}e^{\mathrm{i}t} \tag{2}\]  
where \(N_{0}\) is the number of cells at \(t=0\).  
Figure 1: This image displays the binary fission process [17].  
In the stationary phase, the bacterial growth slows down until it reaches maximum growth and the logarithmic cell number remains constant. The mathematical expression of the stationary phase is expressed as:  
\[\frac{\delta N}{\delta t}=0 \tag{3}\]  
There is a balance between cell division and cell death and there is no actual bacterial growth. This is caused by the depletion of critical nutrients or the accumulation of waste product. Some of the cells can l'use nutrients from the dead cells (endogenous metabolism). This process occurs throughout the whole growth cycle, but occurs in a high degree in the stationary phase. The last phase is called the death or decline phase and accumulation of waste products or exposure to oxygen occurs. The death phase can be mathematically expressed as:  
\[\frac{\delta N}{\delta t}=-k_{d}N \tag{4}\]  
where \(k_{d}\) is the specific death rate.