A rigid pavement is to be designed for a road with an initial PSI of $4\mathrm{.}4$ and a TSI of $2\mathrm{.}5.$ The total lifetime equivalent traffic is estimated to be around $10$ million $18-$kip ESAL. The modulus of subgrade reaction is determined to be $300$ lb$/$in$3.$ Reliability is $95\%,$ the overall standard deviation is $0\mathrm{.}45,$ the concrete's modulus of elasticity is $4\mathrm{.}5$x$106$ psi, the concrete's modulus of rupture is $900$ psi, the load transfer coefficient is $3\mathrm{.}2,$ and

$1)$ Using the diagram provided, determine the required slab thickness $($D$)$ for the concrete slab, rounded to one decimal place. the drainage coefficient is $1\mathrm{.}0.$

$2)$ Then, assuming W$18$ is unknown, and using the slab thickness found in part a$)$ and using the rigid$-$pavement design equation back calculate the total equivalent $18-$kip ESAL, W$18,$ that a concrete pavement with the D value you found could handle.

$3)$ Based on the W$18$ value you will find in part b$),$ which will be different from the initial value given for W$18,$ would the D found in part a$)$ be acceptable? Why or why not? If no$,$ find the proper value for D$.$