A thermally insulated piece of metal is heated under atmospheric pressure by an electric current so that it receives electric energy at constant power $P$. This leads to an increase in the absolute temperature $T$ of the metal with time $t$ as $T(t) = T_0[1 + a(t - t_0)]^{1/4}$, where $a$, $t_0$ and $T_0$ are constants. The heat capacity $C_P(T)$ of the metal is