How do I find the rate constant in this situation?

Say I have two kinds of molecules $A$ and $B$.


The molecules of type $B$ are small and bind onto molecules of type $A$.


(Any number of them may do so, but in practice this number is $\leq 8$.)


We say a molecule of type $A$ is of type $A'$ if it has at least one copy of $B$ bound to it.


More specifically, we say a molecule of type $A$ is of type $A^k$ if it has exactly $k$ copies of $B$ bound to it.


We can easily detect experimentally when a molecule is of type $A'$, but not so easily when a molecule is specifically type $A^3$, for example.


However, it was done at one point, and the researchers gave us a way (given a concentration of $A'$) to determine the individual concentrations of $A^k$'s. (Poisson distribution)


I would like to consider the dissociation reaction $$A^k \rightarrow A^{k-1} + B$$ where $k \geq 1$ and $A^0$ is considered to be $A$.


Because the molecules of $B$ are small, I can assume that the rate of this reaction is independent of $k$ and that the molecules of $B$ dissociate independently of any other molecules of $B$ attached to the same copy of $A$.


My question is: how can I find a constant $c$ so that the rate of the reaction is $r = c[A']$?


