It would depend on the individual kid, the kids that are going with him/her, where they are going, who is driving (or are they flying) etc.
Starting at the top-the individual kid-are you a good responsible person who is worthy of trust? Do you get at least all A's and B's? Do you do what you need to do without being told? Have I ever caught you breaking any rules when I'm not home? Have you gone to any parties/to hang out with friends when I told you not to? Do you usually tell the truth even if you think you will get in trouble? How do you handle peer pressure? Do I see you as someone that will do or don't do whatever I would expect? Or are you easily swayed to join the crowd? Basically have you EARNED the right to be trusted on such a trip?
Next, how about the kids you are going with? Do I know all or most of them? How do I feel about them? Are they a good influence on you? Do you act different in a negative way around any of them? How many people are going? (you and one other person doesn't seem like enough unless the 2 of you are increadibly trust worthy and street smart, 3-5 total would be ideal in my mind, and more than that would be a negative as that many would make risk taking more likely in my mind-you can just be a face in the crowd then).
Where exactly are you going? Are you going to a fairly secluded place? Or will you be around a lot of people most of the day? How far away is it? Is it across the state border that is an hr away, or are you going to the other side of the country? Are you going to a beach? Something like the Hershey Chocolate Factory? Some other type of amusement park? Like going to Cedar Point, Pidgeon Forge or Universal, something where you are actually more looking to ride some rides or something that is also in a fairly well populated area, it's a plus. If it's a beach where I know your primary focus will be on meeting new guys and trying to find some alone time with them, or a beach known for partying, it would significantly lower your chances of going.
How are you getting there? Is this going to be a 4+ hr trip being driven by another 17 year old? Almost certainly you would not be going. Is it only 2 hrs away and you will be driving in shifts? More likely, but still not going to be 100% convinced. Does someone have a 22+ yr old sister who is going to be driving for a few hrs? That sounds better. Or even better are you flying where no young kids will be driving you around? That would be even better.
Also, are you asking me for money? Or, since you are taking an adult trip, are you doing the adult thing and funding your trip yourself? It wouldn't come across as very mature if my kid wanted to go on a trip without a chaperone and have some adult privileges and then asked for money from me to make it happen. If you had a large chunk of money saved that seemed reasonable to pay for most of what you would need for the trip, but wanted a little extra to play safe and are going to pay it back when you come back from the vacation, then that sounds like an adult thing-you have the money, but you want to play safe in case an emergency arose.
It really boils down to the individual circumstances. If you haven't earned my trust, then it's absolutely not. If I feel you have earned the trust necessary to take such a big step so young, and most to all of my above ideals are met, then I would probably let you go. If I trust you, and few to none of my ideals are met, then it would probably still be no, but I would maybe try to find something else to make it up to you.
