$(7$ pts$)$ Suppose the new computer is $1000$ times faster than the current computer you have. Find out how this would affect the running time of algorithms with the following different complexities. S represents the sizes of ingut processed by the current machine and $S^{\text{'}}$ represents the sizes of input processed by the faster machine for the algorithms listed. Express $S^{\text{'}}$ in terms of $S.$

$\backslash$table$[[F(n),S,S,S\%$