Mr:
You can apply the brush to any shape path, and it will follow the path.
1. Make the taper;
2. Drag the tapered shape onto the Brushes palette;
3. Choose "Art Brush", leave everything default for now;
4. Select a path, and apply the Art Brush to it by clicking on it in the palette;
5. Shape the path any way you like, make the stroke bigger or smaller to vary width, etc.
Bert