Battery draining as programs are running in the background of my MacBook Air

If the Mac was completely shut down (confirm the Important note excerpted below) and the battery is becoming completely depleted after only a few days then the battery is defective and needs to be serviced. Contact Apple, here: Batteries - Service and Recycling - Apple.

• Important: If you’re using a Mac laptop, wait for it to shut down completely before closing the display. If you close the display while the Mac is shutting down, it may not shut down properly and may start up more slowly the next time you turn it on.

If programs continue to run then the Mac was not shut down. To learn how to shut down a Mac please read Shut down or restart your Mac - Apple Support. Refer to its first Important note.