An uncharged capacitor is connected in series with a resistor, an ideal battery with potential difference \(V_0 = 10\text{ V}\), and an open switch. At time \(t = 0\), the switch is closed. The graph shows the measured potential difference \(V_C\) across the capacitor as a function of time \(t\) in milliseconds. The potential difference asymptotically approaches \(10\text{ V}\), reaching \(5.0\text{ V}\) at \(t = 2.8\text{ ms}\) and \(6.3\text{ V}\) at \(t = 4.0\text{ ms}\). Based on the graph, what is the time constant \(\tau\) of the circuit?