deletions | additions       diff --git a/2.tex b/2.tex  index bb29b0f..46a945c 100644  --- a/2.tex  +++ b/2.tex 
...
p &= k_1+k_{-1}+k_2+k_{-2}\\  q &= (p^2-4(k_1k_2+k_{-1}k_{-2}+k_1k_{-2}))^\frac{1}{2}  \end{align}  The values of \textit{m} and \textit{n} generally differ by less than an order of magnitude within the range of rate constant values expected for Reaction (1). Thus, fits to time-dependent data in the form of $y(t) &= =  y_0+\Lambda\mathrm{e}^{-\lambda{}t}+K\mathrm{e}^{-\kappa{}t}$ tend to converge to the form $y(t) &= =  y_0+\alpha{}\mathrm{e}^{-\beta{}t}$. We take advantage of this to approximate $\textit{k}_1$ by fitting data for isomer \textit{A} with a single exponential such that equation (5) may be rearranged as: \begin{align}  A(t) &= A_0[\frac{k_{-1}k_{-2}}{k_1k_2+k_{-1}k_{-2}+k_1k_{-2}}+[\frac{k_1k_2+k_1k_{-2}}{k_1k_2+k_{-1}k_{-2}+k_1k_{-2}}]\mathrm{e}^{-x_1t}]  \end{align}