$)$ A memory system consists of single level cache with an access time of $1$ns and a hit rate of $0\mathrm{.}95,$ and main memory with an access time of $60$ns$.$

$($i$)$ Compute the average memory access time $($AMAT$).$

$($ii$)$ If doubling the cache size reduces the miss rate by $30\%$ but increases the cache access time by $10\%,$ what is expected percentage improvement in average memory access time if we double the case size from part $($i$).$