A student investigates the kinetics of the gas-phase decomposition of dinitrogen pentoxide represented by the following equation:

\[ 2\text{ N}_2\text{O}_5\text{(g)} \rightarrow 4\text{ NO}_2\text{(g)} + \text{O}_2\text{(g)} \]

The rate constant \(k\) is measured at several different temperatures, and the data are plotted as \(\ln k\) versus \(1/T\), where \(T\) is temperature in kelvins (\(\text{K}\)). A linear regression of the data yields the best-fit line shown in the graph below, with the equation \(y = -1.20 \times 10^4 x + 30.5\).

Based on these data, what is the activation energy, \(E_a\), for the decomposition reaction? (Use \(R = 8.314\text{ J}/(\text{mol}\cdot\text{K})\))