Chlorine is an effective disinfectant for swimming pools. However, it loses its efficacy by undergoing photochemical decay under bright sunlight. The following is the data collected from a laboratory study.

$\backslash$table$[[$Time $($min$),10,20,30,40,50,60],[$Concentration of $C{l}_2(ppm),2\mathrm{.}45,1\mathrm{.}74,1\mathrm{.}23,0\mathrm{.}88,0\mathrm{.}62,0\mathrm{.}44]]$

$($a$)$ Does the reaction satisfy a power law? If so$,$ show how you would apply the method of half$-$life to measure the order of reaction and the rate constant.

$($b$)$ Assuming ideal exposure conditions, calculate the hourly injection rate $($continuous injection mode$)$ of chlorine to maintain a sterilising $C{l}_2$ level of $1ppm$ by mass in a pool $25,000$ L in volume. Will the amount be lower if chlorine is delivered hourly on an intermittent basis?