  For a polynomial $f(X)=AX^d+C \in \mathbb{F}_p[X]$ with $A\neq 0$ and $d\geq
2$, we prove that if $d\;|\;p-1$ and $f^i(0)\neq f^j(0)$ for $0\leq i<j\leq N$,
then $\#f^N(\mathbb{F}_p) \sim \frac{2p}{(d-1)N},$ where $f^N$ is the $N$-th
iteration of $f$.
