deletions | additions       diff --git a/section_Proofs_subsection_Bacterial_density__.tex b/section_Proofs_subsection_Bacterial_density__.tex  index 1e06758..be6b51e 100644  --- a/section_Proofs_subsection_Bacterial_density__.tex  +++ b/section_Proofs_subsection_Bacterial_density__.tex 
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\end{equation}  \begin{equation}  \dot{\tilde{b}} = \frac{-\dot{N}_B}{N} = f \Gamma_0 \left(\frac{bmc}{a}\right) - \dot{b} m  \end{equation}