$(30$ points$)$ A flexible pavement was designed to have a $6-$inch sand$-$mix asphaltic surface, $8-$inch soil$-$cement base and a $21-$inch crushed$-$stone subbase $($all drainage coefficients are $1\mathrm{.}0).$ The pavement was designed for $100012-$kip single axles and $160034-$kip tandem axles per day in the design direction. Traffic volume increases $2\%$ every year. The reliability used was $90\%,$ the overall standard deviation was $0\mathrm{.}35,$ the initial PSI was $4\mathrm{.}7,$ the TSI was $2\mathrm{.}5$ and the soil resilient modulus was $2600$ psi. If the road has three lanes in the design direction $($and was conservatively designed with a PDL $0\mathrm{.}65),$ for how many years was the pavement designed for?