AB$+$C first order reaction, the following data were obtained in a differential reactor containing W$=5$ g catalyst. k$=3$ m$3/$kg hour$-1$ feed is pure A and the volumetric flow rate is v$=2$ m$3/$hour$.$

a$)$ Calculate the catalyst degradation degree and constant.

b$)$ Considering the catalyst decavitation time, what type of reactor is suitable for this catalyst? Why? Please explain.

$\backslash$table$[[$th$($hour$),0,1\mathrm{.}07,1\mathrm{.}56,2\mathrm{.}04,2\mathrm{.}65,3\mathrm{.}13,3\mathrm{.}69,4\mathrm{.}01,4\mathrm{.}71,5\mathrm{.}11,5\mathrm{.}51,6\mathrm{.}31,7\mathrm{.}11,7\mathrm{.}51,8\mathrm{.}31,8\mathrm{.}71,9\mathrm{.}11,10],[x_a,0\mathrm{.}88,0\mathrm{.}65,0\mathrm{.}58,0\mathrm{.}52,0\mathrm{.}47,0\mathrm{.}43,0\mathrm{.}39,0\mathrm{.}37,0\mathrm{.}34,0\mathrm{.}32,0\mathrm{.}31,0\mathrm{.}28,0\mathrm{.}26,0\mathrm{.}25,0\mathrm{.}23,0\mathrm{.}22,0\mathrm{.}21,0\mathrm{.}19]]$