Induction?? Please help!

I am 38 and expecting our first in about 4 weeks. My Drs have brought up induction for only if I go beyond 40 weeks and a few days. For those who gave birth over 35 with no complications (no GD, no pre-eclampsia or hypertension etc), did you Dr recommend an induction at or earlier than 40 weeks solely because of your age? I did all the Hypnobabies classes and would like to go a few days beyond 40 weeks to see if she will come naturally, my drs have said there is no reason yet to think this isn't fine but I want to know if you've had a different experience.