Order the following four functions with respect to their asymptotic growth $($big$-$

Oh class$)$:

$-A(n)=(6n{)}^n+(n+2{)}^n*(4+n)$

$-B(n)=lo{g}_2(n+8+7^n)*4^{7+3}$

$-C(n)=(10+4n{)}^{10}*\sqrt[\phantom{2}]{n^{4^n}}$

$-D(n)=lo{g}_2(4*\sqrt[\phantom{2}]{2^{lo{g}_2(n)}*n})$

Write your answer as e$.$g$."$A $A(n)=O(B(n))B(n)O(A(n))C(n)D(n)B(n)=O(C(n))C(n)=O(B(n))"$ would $be$ claiming that:

$A(n)=O(B(n))$ but $B(n)O(A(n))(and$ similarly between $C(n)$ and

$D(n))$

$B(n)=O(C(n))$ and $C(n)=O(B(n))",$ where $an$ inequality indicates that the

left hand side $is$ big$-Ohof$ the right$-$hand side but not the other way around, and

$an$ equality indicates that the two functions are big$-Ohof$ each other. $E.g.$ the

hypothetical answer $"A"$ would $be$ claiming that:

$A(n)=O(B(n))$ but $B(n)O(A(n))(and$ similarly between $C(n)$ and

$D(n))$

$B(n)=O(C(n))$ and $C(n)=O(B(n))$

Can you explain the answer and why you get like that?

And can you provide the aymptotic gowth order in general?