We have that
$$ \lim_{x \to \infty} \frac{x^a}{b^x} = 0, \quad a > 0, \quad b > 1$$
So we say that $b^x = o(x^a)$. Meaning that $b^x$ is of higher order that $x^a$.
Q1: What does it mean to have higher order intuitively? Does it mean that one increases/decreases faster than the other one increases/decreases?
Q2: The formel definition have a mathematical structure called an epsilon function.
$$f(x)=\epsilon(x)g(x)$$
What is the epsilon function in my example?