Might be a stupid question- Dating pregnancy

symphonyofblasse@hotmail.com

Just got my BFP yesterday, expecting our first! Something I'm reading conflicting things on is how the dr. estimates how far along you are. For example, I have my first prenatal appointment on Sept. 24th. Does that put me at 9 weeks (last period was July 22nd) or at (almost) 7 weeks (conception was around Aug. 7th). I'm pretty confident on when conception was since I was keeping track of fertile signs, but I know it's never a guarantee, and that's why some drs. will estimate based on your last period. So what I'm really wanting to know is, will we be able to see/hear a heartbeat at that appointment? :-) Thanks for any help!