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+\documentclass{article}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{amsfonts}
+
+\begin{document}
+
+
+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:
+
+\[ \frac{dX}{dt} = \mu X \]
+\[ \frac{dS}{dt} = -q_{S} X \]
+\[ \frac{dP}{dt} = \mu_{P} X \]