Arrange the functions 1.5ⁿ,n¹⁰⁰,(logn)³,√nlogn, 10ⁿ,(n!)² , and n⁹⁹n⁹⁸ in a list so that each function is big-O of the next function.
a) 10ⁿ,n¹⁰⁰,n⁹⁹n⁹⁸,(n!)²,1.5ⁿ,(logn)³,√nlogn
b) 1.5ⁿ,(logn)³,√nlogn,n⁹⁹n⁹68,(n!)²,n¹⁰⁰,10ⁿ
c) 1.5ⁿ,√nlogn,(logn)³,n⁹⁹n⁹⁸,10ⁿ,n¹⁰⁰,(n!)²
d) (logn)³,√nlogn,n⁹⁹n⁹⁸,1.5ⁿ,10ⁿ,n¹⁰⁰,(n!)²