SAT Question 0aaef7aa: Nonlinear Functions answer and explanation with Desmos solution

Choice A is correct. It's given that $p\left(n\right)=7n^3$. Substituting $56$ for $p\left(n\right)$ in this equation yields $56=7n^3$. Dividing each side of this equation by $7$ yields $8=n^3$. Taking the cube root of each side of this equation yields $2=n$. Therefore, when $p\left(n\right)$ is equal to $56$, the value of $n$ is $2$.