 Specific growth rate

The specific growth rate is biomass production per unit existing biomass per unit time. For biomass concentration $x>0$ with growth alone, $\dot{x}=\mu x$ and $\mu =\mathrm{d}(\ln x)/\mathrm{d}t$. A constant positive specific growth rate produces exponential growth, $x(t)=x(0)e^{\mu t}$, with doubling time $\ln 2/\mu$. In a chemostat, removal makes the net rate $\dot{x}/x=\mu (s)-D$, rather than $\mu (s)$ itself.