$6\mathrm{.}5$The current in a $2$ H inductor is

i$=25$A$,$i$=($B$1$cos$5$t$+$B$2$sin$5$t$)$e$$t$$A$,$t$0$;t$0.$

The voltage across the inductor $($passive sign convention$)$ is $100$ V at t$=0.$ Calculate the power at the terminals of the inductor at t$=500$ms$.$ State whether the inductor is absorbing or delivering power.