(a) The variation of resistance, $R$ ohms, of an aluminium conductor with temperature $\theta^{\circ} \mathrm{C}$ is given by $\frac{\mathrm{d} R}{\mathrm{~d} \theta}=\alpha R$, where $\alpha$ is the temperature coefficient of resistance of aluminium. If $R=R_{0}$ when $\theta=0^{\circ} \mathrm{C}$, solve the equation for $R$. (b) If $\alpha=38 \times 10^{-4} /{ }^{\circ} \mathrm{C}$, determine the resistance of an aluminium conductor at $50^{\circ} \mathrm{C}$, correct to 3 significant figures, when its resistance at $0^{\circ} \mathrm{C}$ is $24.0 \Omega$.