I'm writing here because it's more like a math question than $\LaTeX$. I would need to draw some curves like this:
these are curves drawn at different values of a constant parameter $r$. The equation of these curves is
$$ \xi = \dfrac{A_\mathrm{d} \times \exp\left\{-\dfrac{E_\mathrm{A,d}}{RT}\right\} - r } {A_\mathrm{d} \times \exp\left\{-\dfrac{E_\mathrm{A,d}}{RT}\right\} + A_\mathrm{i} \times \exp\left\{-\dfrac{E_\mathrm{A,i}}{RT}\right\}}$$
Where $A_\mathrm{d}, E_\mathrm{A,d}, A_\mathrm{d}, E_\mathrm{A,i}$ and $R$ are constants, with $E_\mathrm{A,d} < E_\mathrm{A,i}$
the independent variable is $T$. These curves were plotted for values of $r$ increasing from the top down. $\xi$ is between 0 and 1, $T$ is between 0 and $\infty$. The asymptotes of any curve for $T$ approches to $\infty$ is
$$ \dfrac{A_\mathrm{d}-r}{A_\mathrm{d}+A_\mathrm{i}} $$
Could you suggest a simplified form of this equation that returns the same curves, so I can use it on pgfplots?