Thank you for the reply. I am actually just changing the settings before I take photos right in the iOS camera app by clicking the 3 gray-scale circles in the bottom right of the camera app, next to the shutter button.
If I email the picture to myself and view it in Gmail on my Windows machine, the thumbnail in the email is B&W but when I download the picture and open it in Windows Photo Viewer it is color. If I download the picture and drag it onto my desktop, the thumbnail is now in color. If I transfer the photos from my iPhone to my Dropbox account using the sync in the Dropbox app, they show up in color. It is like the camera is taking them in color but displaying them in B&W.
If I look at the same email that I sent myself above on the iPhone mail app, the picture is still in B&W. If I save it from the email to my photos on the iPhone it stays in B&W too. It appears that when the photo leaves the apple domain it reverts to color.