Answer
(a)
$$
\mathrm{Q}=8,582 \mathrm{C}
$$
---
(b)
$$ \mathrm{Energy} =90,022 \mathrm{J}$$
Work Step by Step
(a)
$\mathrm{Q}=$ area under the current - time curve $=\int I d t=(3600) \int_{0}^{12} \mathrm{e}^{-5 t / 12} \mathrm{dt}=8,582 \mathrm{C}$
$$
\mathrm{Q}=8,582 \mathrm{C}
$$
---
(b)
$$\quad \frac{\mathrm{d} \mathrm{w}}{\mathrm{dt}}=\mathrm{P}$$
$$w=\int P d t=\int v i d t=(3600) \int_{0}^{12}\left(12-3 \mathrm{e}^{-5 t / 12}\right)\left(\mathrm{e}^{-5 t / 12}\right) d t$$
$$=90,022 \mathrm{J}$$
$$\therefore \mathrm{Energy} =90,022 \mathrm{J}$$
