SAT Question 2c6f214f: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. Since $w$ represents the $n$ th term of the sequence and $9$ is the first term of the sequence, the value of $w$ is $9$ when the value of $n$ is $1$. Since each term after the first is $4$ times the preceding term, the value of $w$ is $9\left(4\right)$ when the value of $n$ is $2$. Therefore, the value of $w$ is $9\left(4\right)\left(4\right)$, or $9{\left(4\right)}^2$, when the value of $n$ is $3$. More generally, the value of $w$ is $9\left(4^{n-1}\right)$ for a given value of $n$. Therefore, the equation $w=9\left(4^{n-1}\right)$ gives $w$ in terms of $n$.