A uniform disk of mass \(M\) and radius \(R\) rotates about a fixed axis through its center. The angular speed of the disk as a function of time \(t\) is given by \(\omega(t) = bt^2\), where \(b\) is a positive constant. What is the ratio of the rotational kinetic energy of the disk at time \(t = 2t_0\) to its rotational kinetic energy at time \(t = t_0\)?