How to add varying thickness in this svg spiral path?

Hello, I am trying to create a simple spiral path using SVG as you see this pen on Codepen but I am looking for a stroke something like this like it should start with a thicker stroke and end with a thinner one giving the sense of depth. Can some one help out as to how I can do that.

A quick Google search came up with this method.
http://owl3d.com/svg/vsw/articles/vsw_article.html

Though it may be simpler to make it a solid filled object instead of using stroke width.

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