The US C-19 case totals are not exponential anymore. They were, but not since about the end of March. The case totals are now growing linearly, or possibly quadratically (with a small constant on the squared term), The daily totals zig-zag all over the place due to extreme randomness on a day-to-day basis, but their trend line (or local regression line, if you want the math term) is pretty much a straight line that is either nearly flat, or maybe is declining very slightly, or maybe is increasing very slightly. With some partial lockdown easing, that may go from trending downward slightly to trending upward slightly, which would mean the totals curve would be accelerating upward.

So for your sentence starting with, "If that rate continues (I'm not saying that it will), ..." we can note that it won't go up exponentially for the time being, it will go up nearly linearly. But if all lockdowns are simply eliminated, then all bets are off.

But in any event, that's a lot better than growing exponentially.