Rogelio has received escalating contract offers from two professional baseball teams. The Turkeys have offered him a yearly salary of $S(t)=80000t$ for $8$ years, while the Hedgehogs have offered him a yearly salary of $S(t)=77000t$ for $9$ years $(t$ is measured in years$).$ Based on the accumulated present value of both contracts, and assuming Rogelio can earn a $3\%$ continuous interest rate on his money, which team has made him a better offer?

The Hedgehogs have made the better offer.

If Rogelio prefers to play for the other team $($the team whose offer was not the best$),$ he should negotiate a signing bonus of dollars in order to make their offer equitable to the better offer. $($Round to the nearest dollar$)$o