In general we say that polynomials grow faster than linear functions. but take the following functions, we have that log^3(n) = o(n). here the linear term grows much faster. however, when we increase the power we get the opposite, e. g. n = o(log^7( where the log term grows faster. how can i determine where the limit lies (or where the equality shifts) for such cases? are there general guidelines to follow?

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You have a linux system that has a 1000gb hard disk drive, which has a 90gb partition containing an ext4 filesystem mounted to the / directory and a 4gb swap partition. currently, this linux system is only used by a few users for storing small files; however, the department manager wants to upgrade this system and use it to run a database application that will be used by 100 users. the database application and the associated data will take up over 200gb of hard disk space. in addition, these 100 users will store their personal files on the hard disk of the system. each user must have a maximum of 5gb of storage space. the department manager has made it very clear that this system must not exhibit any downtime as a result of hard disk errors. how much hard disk space will you require, and what partitions would you need to ensure that the system will perform as needed? where would these partitions be mounted? what quotas would you implement? what commands would you need to run and what entries to /etc/fstab would you need to create? justify your answers.

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