Modeling
Mutagenesis Induction
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$$ \frac{\partial c_{A_{L}}(t)}{\partial t} = \Phi_{A} \cdot c_{A_{S}} - \Phi_{L} \cdot c_{A_{L}(t)} $$ \(\Phi_{A}\) and \(\Phi_{L}\) are measured relative to the lagoon volume. For a steady state, the above equation results in
$$ c_{A_{L}}(t) = \frac{\Phi_{A}}\{\Phi_{L}} \cdot c_{A_{S}} $$
However, in some cases it may be relevant to estimate when a given percentage of the equilibrium concentration is reached. To make statements about that, the differential equation is solved to
$ c_{A_{L}} (t) = \Phi_{A} \cdot c_{A_{S}} \cdot t - e^{-\Phi_{L} \cdot t} $$ }} }}
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References