A computer system has a two$-$level memory hierarchy comprising a cache and main memory. The cache has an access time of $5$ nanoseconds, while the main memory has an access time of $80$ nanoseconds. The hit rate for the cache is $90\%.$

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Calculate the Effective Memory Access Time $($EMAT$)$: Using the hit rate and access times, calculate the EMAT for this system.

Impact of Cache Hit Rate on Performance: Calculate the EMAT again if the cache hit rate drops to $80\%.$ How does this change in hit rate affect the EMAT? Explain briefly why maintaining a high hit rate is essential for system performance.