A $2\mathrm{.}40$ M$$ resistor and a $0\mathrm{.}990$F capacitor are connecte in series with an ideal battery of emf E$=5\mathrm{.}00$V$.$ At $0\mathrm{.}816$s after the connection is made, what is the rate at which $($a$)$ the charge of the capacitor is increasing, $($b$)$ energy is being stored in teh capacitor, $($c$)$ thermal energy is appearing in teh resistor, and $($d$)$ energy is being delivered by the battery?