A stage construction is planned for a full$-$depth asphalt pavement with a subgrade resilient modulus of $5000$ psiThe design period is $30$ years and is divided into three stages: the first $5$ years, the middle $10$ years, and the last $15$ years. The first year traffic on the design lane is $30,000$ equivalent $18-$kip single$-$axle load applications, and the annual growth rate is $4\%.$ If the damage ratios at the end of each stage are $0\mathrm{.}5,0\mathrm{.}75,$ and $1\mathrm{.}0,$ respectively, determine the thicknesses of HMA to be placed in ach stage by the Asphalt Institute method