$(9\%)$ After decades, BSE finally has saved the necessary funds to build a new building. The preliminary subsurface geological investigation of the site suggests that a $5-$ft thick normally consolidated clay layer is located between two sand layers. The analyses of core samples indicate a void ratio of $0\mathrm{.}9$ and a compression index of $0\mathrm{.}35.$ Assume the building increases the existing average stress in the layer from $1000$ psf to $3000$ psf$.$ What is the settlement of clay layer?