You wouldn't see exponential growth, though. You wouldn't even see linear growth. Not if the populace has already seen how to kill the things over YouTube, and communication systems are still largely intact.
I'm not arguing there'd be no instances of outbreaks. Sure - someone young and healthy has a stroke in the middle of a neighborhood - some families gets wiped out. But those kinds of stresses don't lead to societal breakdown.
Looking at my math a different way - each day right now 1 out of every 45,000 people die. Are you saying those 44,999 other people can't handle it if that death becomes somehow contagious? And not airborne contagious - contagious via staggering, brainless corpses?
I think you're taking an over simplified view of what could happen. Do you really think its more likely that people instantly grab their hammers and bats to organize a defense vs. disbelief, fear, rioting, and giving up? Think through all of the zombie/contagion/apocalypse movies we've seen. When this starts, the vast majority of people won't believe its real. Would you? It might take weeks just to convince people it's happening. As people figure out something is wrong, they'd likely shut themselves in for fear of contamination. You're assuming people will just fight back, but I think most people without training would freeze when confronted with a zombie, just like most due in extremely traumatic real life situations.
Either way, you can clearly count on massive work stoppage and looting. Take the 7,000 that would have died anyway, plus the increased deaths from people that can't get their meds, health care, rioting, etc. Who is delivering fresh groceries or manning the water treatment plant? How about the power plants? Take away food and power for just a few weeks and you'd see any sense of law and order fly out the window. Add to that the killings from people who think someone is sick and could infect them, people fighting each other for resources, suicide, etc. People also wouldn't know that zombie bites are fatal or that people dying from other causes will come back, so many would try to care for the sick and wounded only to get surprise attacked later. Think about mass population centers where a hoard of zombies could grow fairly quickly. It's easy to think 20 people could stop a zombie, but 20 zombies vs. one person is very different.
Social media can spread disinformation as quickly as good information and a fair amount of people aren't getting their news from Youtube. Reference the movie Contagion. Those that can figure out how to kill a zombie still need to be able to do it in real life. Not as easy to kill a loved one, especially for those that think there might be some kind of cure. Reference TWD Morgan and Hershel. I do think there would be more of a resistance than we've seen in the shows. There would be pockets of communities or safe houses that could band together and set up procedures to keep watch, reduce the risk of an outbreak, etc. But there's potential for those to break down in short order as well once people start fighting over scarce resources, weapons, authority, etc. Someone gets careless or has an unexpected death or some virus spreads without treatment.
Anyway, I don't think we're going to convince each other. Hopefully we'll never have to find out.