QP$28512.$ "Permeability is a critical property in the design and performance assessment of landfill liners, as it determines the rate at which fluids can pass through the composite material. Landfill liners are typically composed of multiple layers of different materials, each with its own permeability and thickness. These layers work together to minimize the leakage of hazardous substances into the surrounding environment, protecting soil and groundwater from contamination.

Consider a composite material used in a landfill liner composed of following distinct layers, each with specific thickness and permeability properties. The properties of the layers are summarized in the following table:

$"$

Layer Thickness $($m$)$ Permeability $($ m$/$day$)$ Layer Thickness $($m$)$ Permeability $($ m$/$day$)$ Layer Thickness $($m$)$ Permeability $($ m$/$day$)$

$10\mathrm{.}24033\mathrm{.}544642\mathrm{.}5401520\mathrm{.}34101204\mathrm{.}2403337\mathrm{.}54$

$20\mathrm{.}30066\mathrm{.}584744\mathrm{.}4001553\mathrm{.}38102208\mathrm{.}3003370\mathrm{.}58$

$30\mathrm{.}40099\mathrm{.}624846\mathrm{.}3001586\mathrm{.}42103212\mathrm{.}4003403\mathrm{.}62$

$40\mathrm{.}540132\mathrm{.}664948\mathrm{.}2401619\mathrm{.}46104216\mathrm{.}5403436\mathrm{.}66$

$50\mathrm{.}720165\mathrm{.}75050\mathrm{.}2201652\mathrm{.}5105220\mathrm{.}7203469\mathrm{.}7$

$60\mathrm{.}940198\mathrm{.}745152\mathrm{.}2401685\mathrm{.}54106224\mathrm{.}9403502\mathrm{.}74$

$71\mathrm{.}200231\mathrm{.}785254\mathrm{.}3001718\mathrm{.}58107229\mathrm{.}2003535\mathrm{.}78$

$81\mathrm{.}500264\mathrm{.}825356\mathrm{.}4001751\mathrm{.}62108233\mathrm{.}5003568\mathrm{.}82$

$91\mathrm{.}840297\mathrm{.}865458\mathrm{.}5401784\mathrm{.}66109237\mathrm{.}8403601\mathrm{.}86$

$102\mathrm{.}220330\mathrm{.}95560\mathrm{.}7201817\mathrm{.}7110242\mathrm{.}2203634\mathrm{.}9$

$112\mathrm{.}640363\mathrm{.}945662\mathrm{.}9401850\mathrm{.}74111246\mathrm{.}6403667\mathrm{.}94$

$123\mathrm{.}100396\mathrm{.}985765\mathrm{.}2001883\mathrm{.}78112251\mathrm{.}1003700\mathrm{.}98$

$133\mathrm{.}600430\mathrm{.}025867\mathrm{.}5001916\mathrm{.}82113255\mathrm{.}6003734\mathrm{.}02$

$144\mathrm{.}140463\mathrm{.}065969\mathrm{.}8401949\mathrm{.}86114260\mathrm{.}1403767\mathrm{.}06$

$154\mathrm{.}720496\mathrm{.}16072\mathrm{.}2201982\mathrm{.}9115264\mathrm{.}7203800\mathrm{.}1$

$165\mathrm{.}340529\mathrm{.}146174\mathrm{.}6402015\mathrm{.}94116269\mathrm{.}3403833\mathrm{.}14$

$176\mathrm{.}000562\mathrm{.}186277\mathrm{.}1002048\mathrm{.}98117274\mathrm{.}0003866\mathrm{.}18$

$186\mathrm{.}700595\mathrm{.}226379\mathrm{.}6002082\mathrm{.}02118278\mathrm{.}7003899\mathrm{.}22$

$197\mathrm{.}440628\mathrm{.}266482\mathrm{.}1402115\mathrm{.}06119283\mathrm{.}4403932\mathrm{.}26$

$208\mathrm{.}220661\mathrm{.}36584\mathrm{.}7202148\mathrm{.}1120288\mathrm{.}2203965\mathrm{.}3$

$219\mathrm{.}040694\mathrm{.}346687\mathrm{.}3402181\mathrm{.}14121293\mathrm{.}0403998\mathrm{.}34$

$229\mathrm{.}900727\mathrm{.}386790\mathrm{.}0002214\mathrm{.}18122297\mathrm{.}9004031\mathrm{.}38$

$2310\mathrm{.}800760\mathrm{.}426892\mathrm{.}7002247\mathrm{.}22123302\mathrm{.}8004064\mathrm{.}42$

$2411\mathrm{.}740793\mathrm{.}466995\mathrm{.}4402280\mathrm{.}26124307\mathrm{.}7404097\mathrm{.}46$

$2512\mathrm{.}720826\mathrm{.}57098\mathrm{.}2202313\mathrm{.}3125312\mathrm{.}7204130\mathrm{.}5$

$2613\mathrm{.}740859\mathrm{.}5471101\mathrm{.}0402346\mathrm{.}34126317\mathrm{.}7404163\mathrm{.}54$

$2714\mathrm{.}800892\mathrm{.}5872103\mathrm{.}9002379\mathrm{.}38127322\mathrm{.}8004196\mathrm{.}58$

$2815\mathrm{.}900925\mathrm{.}6273106\mathrm{.}8002412\mathrm{.}42128327\mathrm{.}9004229\mathrm{.}62$