$2$ Use the data in the exhibit to complete the two tasks below. Exhibit: Factors of Production Data Period Y K L Share of Labor in Output $11002001000\mathrm{.}521072051020\mathrm{.}531112101040\mathrm{.}54110\mathrm{.}52151040\mathrm{.}551102201040\mathrm{.}5$ a$.$ Compute and report the value of growth in total factor productivity $(($At$$At$1)/$At$1)$ in each period from periods $2$ through $5.$ Assume that the value of A is $1\mathrm{.}000$ in period $1.$ Report the value of A in each period. b$.$ Does the value of A rise in each period? If it declines, do you think this decline is because technological progress works backward? If so$,$ explain your answer. If not, provide another explanation.