If I should charge, how much would be good price? I think it will take my team a cumulative of 15 hours. The potential client has not paid anything yet. I know some people would do this job for free in hopes of getting the business but I don't want to work for free.
Completely agreed with Evan. The only time I would ask a shop to do work without money being exchanged is when they're taking equity in a project. A blended rate of $79 per hour is at the mid point of reasonableness and $120-$150 per hour would be the high point.
If you're asking about rates, it sounds like you don't have a lot of experience building mobile apps so if that's the case, I'd suggest you charge the low end of the range because it has the potential to act as a big reference account for you. If on the other hand, I'm reading the situation incorrectly, then charge whatever your normal rate is.
I refer a lot of work to a couple of mobile app shops I trust and like and have previously worked at an interactive agency. Happy to talk to you in a call to give you more perspective and clarity.
Best of luck!