It will rise until it peaks and then be replaced by the next hype.

I think that is true for all the technologies.... 

Of course, but your question is not precise enough to give a more concrete answer IMHO.

I think It will  go up at least in next 10 years. The whole architecture may not have change, but the detail will change simultaneously with advances in brain study because it is biologically inspired.I think deep learning is a concept and does not refer to any specific techniques. Any network with many layers is called deep learning.

logarithmic growth

https://www.slideshare.net/mohamedloey/deep-learning-71352250

Deep learning will be hot topics for at least 10 years

This is a bit outdated but provides input on future trend, as suggested by top researches in deep learning as of 2015.Any similar link with more updated version will be better, but for now, here is the link: https://www.kdnuggets.com/2016/01/deep-learning-2016-beyond.html