Exponential growth

Exponential growth can be observed in nature when resources are in surplus. It is characterized by a constant growth rate (μ). The growth rate of a population that grows exponentially can be determined from the slope of the following logarithmic plot:

Exponential cell growth can be described by this equation:

Note that the change in biomass is dependent on the concentration of biomass. Integration of the formula gives the following:

As seen, from the equation, μ_max can be found in a plot of ln(x) versus time. The intercept of this plot will be ln(x₀), and the slope will be μ_max, also called the maximum specific growth rate.

Doubling time of cells is the time it takes for the biomass concentration to double. It can be calculated using the formula below:

Abbreviations

x: cell concentration (g l^-1)
t: time of incubation (h)
μ: specific growth rate (h^-1)
x_o: cell concentration at time zero or inoculum size (h)
t₂: cell doubling time