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They say that battery tech has been improving at 2% a year.

That would mean we should see a ~37% improvement between 2008 and 2016. Seems about right.

That's not a "fivefold improvement". A fivefold improvement is 400% more.

Maybe the battery form factors that are being improved aren't appropriately sized for use in smartphones? :)

1.02^8=1.17, or ~17% improvement

errr, oops. I did ^16 by accident. Damn you human error!

Do you work at NASA?