I read this chapter sitting in an airport thinking I was inconvenienced by travel! God used it to put me at peace.
The decision maker was more persuaded by the captain/owner than by Paul. Paul had a series of accurate predictions that earned him credibility with the captain and crew, even though some of them gave up hope of ever being saved.
The storm went on for over 14 days. Did Paul pray for it to be over? It doesn't say he did.
He received a vision, shared it and comforted the sailors. Some circumstances actually cause professional sailors to listen to a preacher.
None of the prisoners were killed because the captain wanted to save Paul -- Interesting influence. Just as he predicted, everyone made it safely to the beach.