> Problem with exponential growth is that you can be a little off in the exponent and be totally off in the result.

Which is why the growth rate is really what matters. Which isn't immutable. It goes down if people wash their hands. It goes down if sick people stay at home.

This is also why it really matters if the rate is 150% or 130%, even if both are very bad, because the higher rate is very worse. And the rate gets lower if sick people stay home, but it gets higher if idiots panic and start hoarding masks and stealing hand sanitizer which increases the rate of infection when they aren't there for other people to use.

Panic is not just useless, it's actively harmful.

Not really, only if you don't recalibrate every so often... but this can happen in any kind of growth. Even linear growth with unequal coefficients diverges after some amount of time, exponential growth just gets there faster.

This is so wrong. The ratio between exp(x+ϵ) and exp(x) for even ϵ arbitrarily close to zero is infinity in the limit of large x. There is nothing like it with any polynomial growth for any exponent. The ratio between (x+ϵ)^p and x^p for arbitrarily large p is 1 in the limit of large x, for any ϵ.

Another sign that people don't get exponential growth, even if they think they do.

The ratio is, but the absolute value difference (which is what actually matters for humans) grows beyond bounds for both.