A period of time in which microbial cells grow at a constant maximum rate, unrestricted in terms of nutrients or substrate such that there is a repetitive doubling of cells. After inoculation of a bioreactor with living cells, there is an initial lag phase in which the cells adjust to their new environment. There is then an acceleration phase until the cells begin to grow at their maximum rate. The increase in population is then expressed as:

Integrating from an initial population N_o at time t = 0, gives $t=\frac{1}{k}\ln \left(\frac{N}{N_o}\right)$. It can also be expressed as $N=N_{\mathrm{o}}{e}^{kt}$ and alternatively is known as the exponential phase.