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pirt:
\[ q_{S} = \frac{\mu}{Y_{X/S}} + m_{S} \]

monod:
\[ \mu(S) = \frac{\mu_{\max} S}{K_{S} + S} \]

moser:
\[ \mu(S) = \frac{\mu_{\max} S^n}{K_{S}^n + S^n} \]

contois:
\[ \mu(S,X) = \frac{\mu_{\max} S}{K_{S} X + S} \]

bergter:
\[ \mu(S,t) = \frac{\mu_{\max} S}{K_{S} + S} \left(1 - e^{-t/T}\right) \]

Aiba:
\[ \mu(S) = \mu_{\max} \frac{S}{K_S + S} e^{-K_I S} \]

Andrews:
\[ \mu(S) = \mu_{\max} \frac{S}{K_S + S + \frac{S^2}{K_I}} \]

Tessier:
\[ \mu(S) = \mu_{\max} \left(1 - e^{-S/K_S}\right) \]

Equações de Massas:

\[ \frac{dX}{dt} = \mu X \]
\[ \frac{dS}{dt} = -q_{S} X \]
\[ \frac{dP}{dt} = \mu_{P} X \]