Suppose your company has five algorithms, $A_1,A_2,A_3,A_4$ and $A_5$ for five important applications. Given

input size $n,$ their respective running time are exactly $logn,n,n^2,n^3,$ and $2^n.$ The computer currently in

use can solve, using one hour, problems of respective maximum sizes $S_1,S_2,S_3,S_4,S_5.$

Your company plans to get a new computer, which runs $k$ times faster than the current one. As a result,

the maximum problem sizes these algorithms can solve in one hour will increase. For example, the maximum

problem size solved by $A_2$ will become $k*S_2.$

Please calculate the new maximum problem sizes solved by $A_1,A_3,A_4$ and $A_5$ in one hour with the new

computer and show your work.