In the circuit shown, an ideal battery of potential difference \(\Delta V_0 = 12\text{ V}\) is connected in series with an open switch \(S\) and resistor \(R_1 = 10\text{ }\Omega\). A parallel combination consisting of resistor \(R_2 = 20\text{ }\Omega\) and an initially uncharged capacitor \(C = 50\text{ }\mu\text{F}\) is connected in series with \(R_1\). At time \(t = 0\), switch \(S\) is closed, and the potential difference \(V_C\) across the capacitor is recorded as a function of time \(t\), producing the graph shown. Which of the following statements correctly interprets the features of the graph regarding the circuit's behavior?