I must say I really question your use of the term "layman". I am a CEO of ideasware, focused on consulting for AI, robotics, and nanotechnology companies. For 8 years before them I was CEO of memememobile . com, which had patents on individually trained voice recognition. I personally raised $3 Million, and sold it off for a very handsome profit. Previously I worked as Director of ERM at Siebel, CTO at Cipient, Director at KPMG, long-term consultant (3 years) at Cisco, and Manager at Disney. I am not, by any means, a fool. When I say "exponential growth" I specifically mean as recognized by Ray Kurwzeil, Director at Google, and many of his AI friends. It's pretty much a given that for information sciences, Moore's Law has been around for 50 years, dropping 50% each 18 months, without exception. For the past 110 years it has been like that (check your youtube to see, it's quite obvious), and experts predict it will be like that for quite some time in the future.
If you'd like to argue with authority, here's a deep mind researcher talking about the question, saying much the same as what I have on AI needing data. It's about ten minutes in.