Squeeze array animated shape?

Hi folks,

Please take a look at the vid linked below.

In it, i’ve created a plane, then used an array and curve to create an animation.

What i would actually like is that as the animation proceeds, the shape should get thinner so that it actually extrudes into a point.

So my question is, is it somehow possible to put the whole thing in some kind of “container” and then transform that (squeeze it thinner at one end)?

And if not, how could one achieve such a thing (animation)?