  For a graph $G,$ we consider $D \subset V(G)$ to be a porous exponential
dominating set if $1\le \sum_{d \in D}$ $\left( \frac{1}{2}
\right)^{\text{dist}(d,v) -1}$ for every $v \in V(G),$ where dist$(d,v)$
denotes the length of the smallest $dv$ path. Similarly, $D \subset V(G)$ is a
non-porous exponential dominating set is $1\le \sum_{d \in D} \left(
\frac{1}{2} \right)^{\overline{\text{dist}}(d,v) -1}$ for every $v \in V(G),$
where $\overline{\text{dist}}(d,v)$ represents the length of the shortest $dv$
path with no internal vertices in $D.$ The porous and non-porous exponential
dominating number of $G,$ denoted $\gamma_e^*(G)$ and $\gamma_e(G),$ are the
minimum cardinality of a porous and non-porous exponential dominating set,
respectively. The consecutive circulant graph, $C_{n, [\ell]},$ is the set of
$n$ vertices such that vertex $v$ is adjacent to $v \pm i \mod n$ for each $i
\in [\ell].$ In this paper we show $\gamma_e(C_{n, [\ell]}) = \gamma_e^*(C_{n,
[\ell]}) = \left\lceil \tfrac{n}{3\ell +1} \right\rceil.$
