Macbook Air battery drains unusually fast

Hi All!

My one year old Macbook Air (mid 2013) battery is drainage fast after what seems to have been my update to OS X 10.9.5.

When checking the Activity Monitor, as suggested by other blogs, i noticed a CPU usage of 100% or more by "Safari Web Content (Not Responding)" written in red. (screen shot attached). If I'm in Safari, my battery drains about 1% every 3 minutes.

If I shut down and restart, the activity monitor will be okay for about 10-15 minutes, and then it shows up again.

I ran a Diagnostics test...nothing! I cleared my cache as suggested by others...nothing! I ran a Safari update that was due...nothing! I even reset the SMC....nothing!

Any suggestions before I take it to our Apple dealer here in Greece...which I'm dreading....

Much appreciated!

P.S. I'm not the most literate when it comes to Apple hardware and tech talk...so you'll have to lead me step by step....