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.