Given Information:The time taken by algorithm to solve the problems in f(n) microseconds.

Explanation:

Since 1 microsecond is equal to 10−6 seconds. Therefore, 1 second is equal to 106 microseconds.

Consider the function f(n)=lg(n) . Now, determine the value of n such that lgn<106

as follows:

lgn<1062lgn<2 106n<2 106

Therefore, the value of n is 2106 for 1 second.

Since 1 hour is equal to 3600 seconds. Therefore, 1 hour is equal to 3.6×109 microseconds.

Again, consider the function f(n)=lg(n) . Now, determine the value of n such that lgn<3.6×109

as follows:

lgn<3.6×1092lgn<23.6× 109n<23.6× 109

Therefore, the value of n is 23.6×109 for 1 hour.

Consider a month is equal to 30 days and a year is equal to 365 days.

Similarly, calculate the other values of t in the different functions f(n) to obtain the correspondinglargest values of n .

Complete the table for different values of n

as follows:

f(n)	1 second	1 minute	1 hour	1 day	1 month	1 year	1 century
lgn	2106	26×107	23.6×109	28.64×1010	22.592×1012	23.15×1013	23.16×1015
n	1×1012	3.6×1015	1.29×1019	7.46×1021	6.72×1024	9.95×1026	9.95×1026
n	1×106	6×107	3.6×109	8.64×1010	2.59×1012	3.15×1013	3.16×1015
nlgn	62746	2801417	133378058	2755147513	71870856404	797633893349	6.86×1013
n2	1000	7745	60000	293938	1609968	5615692	56176151
n3	100	391	1532	4420	13736	31593	146679
2n	19	25	31	36	41	44	51
n!	9	11	12	13	15	16	17

Table 1