$1.(20$pt$)$ Decide the time complexity of the following running time functions using Big$-$O notations $($using the lowest $($closest$)$ upper bound$).$ Note that logn is a shorthand notation for logan$.$ Order the running time functions by the growth rate in increasing order. Write a rank number for the function. Number $1$ is for the function with the lowest growth rate $($Number $0$ is given as an example below$).$ Use the same number to indicate the same growth rate.

Rank $0$

Function

F$1$:$5$

F$2$: n$^3+1024$n

F$3$: $100$nlogn $+1024$n$2$

F$4$: $2"+1024$n$4$

F$5$: $1024$n $+($logn$)100$ F$6$: $100$nlogn $+1024$n

Lowest upper bound using Big$-$O O$(1)$