SAT Question 161126cf: Nonlinear Functions answer and explanation with Desmos solution

Choice A is correct. The equation $f\left(x\right)={\left(1.84\right)}^{\frac{x}{4}}$ can be rewritten as $f\left(x\right)={\left(1.84\right)}^{\left(\frac{1}{4}\right)\left(x\right)}$, which is equivalent to $f\left(x\right)={\left(1.84^{\frac{1}{4}}\right)}^x$, or approximately $f\left(x\right)={\left(1.16467\right)}^x$. Since it's given that $f\left(x\right)={\left(1.84\right)}^{\frac{x}{4}}$ can be rewritten as $f\left(x\right)={\left(1+\frac{p}{100}\right)}^x$, where $p$ is a constant, it follows that $1+\frac{p}{100}$ is approximately equal to $1.16467$. Therefore, $\frac{p}{100}$ is approximately equal to $0.16467$. It follows that the value of $p$ is approximately equal to $16.467$. Of the given choices, $16$ is closest to the value of $p$.