Question

Arrange the following expressions by growth rate from slowest to fastest.

4n² ; log₃n ; n! ; 3ⁿ ; 20n ; 2; log₂n; n^2/3 ;   n² + 3n + 7 ; 4n^3/2 ;   log₂n * log_{2n ;} nlog₂n + 200n

Format your answer by writing one or more functions on each line of your answer, with slower growing
functions appearing first. Functions that grow at the same asymptotic rate as one another should be placed
together on the same line of your answer.

Thank you!

Answer 1

Growth rate from slowest to fastest

n! n=10 ,10!=10*9*8*7*6*5*4*3*2*1=3628800

3^{n n=10 ,3^10=3*3*3*3*3*3*3*3*3*3 =}59049

4n² , n² + 3n + 7 n=100 ,4*100^2=40000 n=100 , 100^2+ 3*100 +7=10307

nlog₂n + 200n n=100 ,100*log(100) + 200*100=664.38+20000=20664.38

4n^{3/2 n=100 , 4*(100)^3/2=4*10^3=4000}

20n n=1000 , 20*1000=20000

n^{2/3 n=1000 , (1000)^2/3= 10^2=100}

log₂n * log₂n _{n=1000 , log(1000)*log(1000)=}9.965*9.965= 99.301225

log₂n n=1000 , log(1000)=9.965

log₃n n=1000 , log(1000)= 6.28

2