One way to accomplish what you're trying to do is using proportional editing.
- Select the ending edge loop and fill it
- Poke the face
- Subdivide with
several cuts
- Select the center group of faces or just the center
point
- Enable proportional editing
- Move (locked to one direction) and
adjust the "sphere of influence" until it looks as desired.
I've attached a gif of the process. This example has way too many faces but that can be fixed w/ some simple limited dissolving later.
http://i.imgur.com/TRfjowS.gifv
I've also included a gif of the different menus I used during the process.
- Select Similar - SHIFT + g
- Faces - CTRL + f
- Proportional Editing and Options
- Use your scroll wheel to adjust the influence of the editing
http://imgur.com/fLwo5g6.gifv