In a batch reactor $0\mathrm{.}4\%$ of liquid A decomposes in $20$ seconds when C A $=4\mathrm{.}0$ mol$/$L$.$ The

same amount of A $(0\mathrm{.}4\%)$ decomposes in $10$ seconds when C A$=16\mathrm{.}0$ mol$/$L$.$ Find the rate

equation to represent the decomposition of A$.$