1-1 Comparison of running times

1-1

For each function $f(n)$ and time $t$ in the following table, determine the largest size $n$ of a problem that can be solved in time $t$, assuming that the algorithm to solve the problem takes $f(n)$ microseconds.

Function	1 second	1 minute	1 hour	1 day	1 month	1 year	1 century
$lg n$	$2^{10^6}$	$2^{6 \times 10^7}$	$2^{3.6 \times 10^9}$	$2^{8.64 \times 10^{10}}$	$2^{2.59 \times 10^{12}}$	$2^{3.15 \times 10^{13}}$	$2^{3.15 \times 10^{15}}$
$\sqrt n$	$10^{12}$	$3.6 \times 10^{15}$	$1.3 \times 10^{19}$	$7.46 \times 10^{21}$	$6.72 \times 10^{24}$	$9.95 \times 10^{26}$	$9.95 \times 10^{30}$
$n$	$10^6$	$6 \times 10^7$	$3.6 \times 10^9$	$8.64 \times 10^{10}$	$2.59 \times 10^{12}$	$3.15 \times 10^{13}$	$3.15 \times 10^{15}$
$n lg n$	$6.24 \times 10^4$	$2.8 \times 10^6$	$1.33 \times 10^8$	$2.76 \times 10^9$	$7.19 \times 10^{10}$	$7.98 \times 10^{11}$	$6.86 \times 10^{13}$
$n^2$	1,000	7,745	60,000	293,938	1,609,968	5,615,692	56,156,922
$n^3$	100	391	1,532	4,420	13,736	31,593	146,645
$2^n$	19	25	31	36	41	44	51
$n!$	9	11	12	13	15	16	17