Was ist denn das Original, D oder E?

So passen beide in der Tat nicht zusammen.

Accelerating interest wäre ein immer schneller zunehmendes Interesse.

Growing oder increasing bezieht sich unmittelbar auf die Wachstumsgeschwindigkeit, acceleration ist die erste Ableitung davon.

Some people use "accelerating" this way. It kind of bugs me, but I see it’s even made the NY Times (their venerable London uncle only has it once, in a quotation, but then, they are not exactly known for their modern, edgy language ...) .

To me accelerating means "gaining speed", so I read "accelerating interest" as a kind of ellipsis, meaning, as in #1, "interest growing at an increasing rate" or (in a transitive sense) "hastening the growth of interest."

That reminds me, it might be helpful to note that zunehmend does not have a transitive sense whereas "increasing" and "accelerating" both do. Sometimes this ambiguity can be useful.

"Rising" and "burgeoning " do not have transitive meanings.

Edit: burgeoning doesn't sound very modern or edgy either, though, I'd advise against it....