SAT Question 99269e03: Nonlinear Functions answer and explanation with Desmos solution

Choice B is correct. It's given that the table shows three values of $x$ and their corresponding values of $y$ for the equation $y=4{\left(2\right)}^x+3$. It's also given that when $x=3$ the corresponding value of $y$ is $a$, and $a$ is a constant. Substituting $3$ for $x$ and $a$ for $y$ in the given equation yields $a=4{\left(2\right)}^3+3$, or $a=35$. Therefore, the value of $a$ is $35$.