$(25$ points$)$ After turning off the engine, an impeller has an angular velocity of $($t$)=13\mathrm{.}0$ e$-0\mathrm{.}72$t where $13\mathrm{.}0$ is in rad$/$s and $0\mathrm{.}72$ is in s$-1.$ Find the angular acceleration at t $=1\mathrm{.}0$ s and the total number of revolutions the impeller will make.