SAT Question a9084ca4: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. The y-intercept of a graph in the xy-plane is the point where $x=0$. For the given function $f$, the y-intercept of the graph of $y=f\left(x\right)$ in the xy-plane can be found by substituting $0$ for $x$ in the equation $y=9,000{\left(0.66\right)}^x$, which gives $y=9,000{\left(0.66\right)}^0$. This is equivalent to $y=9,000\left(1\right)$, or $y=9,000$. Therefore, the y-intercept of the graph of $y=f\left(x\right)$ is $\left(0,9,000\right)$. It's given that the function $f$ models the number of advertisements a company sent to its clients each year. Therefore, $f\left(x\right)$ represents the estimated number of advertisements the company sent to its clients each year. It's also given that $x$ represents the number of years since $1997$. Therefore, $x=0$ represents $0$ years since $1997$, or $1997$. Thus, the best interpretation of the y-intercept of the graph of $y=f\left(x\right)$ is that the estimated number of advertisements the company sent to its clients in $1997$ was $9,000$.