Accidentally Suggested a Really Expensive Date.. Help!

So I went out with someone for the first time, and it was wonderful. We hit it off and it's obvious that we like each other a lot. So I suggested another date in which we do something that she mentioned on the first date (let's call it racquetball), and she promptly accepted and said she was excited, which was awesome. But then I realized that this activity is actually very expensive, and since I suggested the date, I feel like it's my responsibility to pay for both of us. It would be close to $100, which I think is excessive for a second date where both parties are young and probably don't make a lot (I know I don't). I know it was really stupid of me to suggest this activity before checking how much it would actually cost, but I guess I just assumed that it would be reasonable, and I was excited because it seemed like the perfect idea since she specifically mentioned being interested in doing it. What should I do? If I go back on it now, I'll look like a jerk who doesn't want to pay for anything.