$(15$ points$)$ The decomposition of a reactant A into $B$ and $C$ is held in a fixed$-$volume batch reactor.

$AB+C$

$(1)(5$ pts$)$ Suggest the rate law if the rate law is apparent first order at high concentration of A and

apparent second order at low concentration of A$.$

$(2)(5$ pts$)$ Suggest the rate law if the concentration of A decreases linearly with time.

$(3)(5$ pts$)$ Suggest the rate law if the concentration of A decreases exponentially with time.