The characteristic of exponential is that things tend to come all once. In the final double period, you get as many cases as all the other doubling periods combined.
Which is to say, you can stretch out exponential growth a lot and still not have enough. If you exponential growth from 1,000 to 1,000,000 cases over a year, the last month will overwhelm your services entirely and constitute the bulk of both cases and death.
There's a reason all those early graphs showed parabolas, not actual exponential curves, you can't even give plausible visual representation of this process, because it isn't plausible.
Which is to say, you can stretch out exponential growth a lot and still not have enough. If you exponential growth from 1,000 to 1,000,000 cases over a year, the last month will overwhelm your services entirely and constitute the bulk of both cases and death.
There's a reason all those early graphs showed parabolas, not actual exponential curves, you can't even give plausible visual representation of this process, because it isn't plausible.