SAT Question 281a4f3b: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. Because the change in the number of students decreases by the same percentage each year, the relationship between the number of students and the number of years can be modeled with a decreasing exponential function in the form $f(x)=a(1-r{)}^x$, where $f(x)$ is the number of students, $a$ is the number of students in $2015$, $r$ is the rate of decrease each year, and $x$ is the number of years since $2015$. It's given that $3,000$ students were enrolled in $2015$ and that the rate of decrease is predicted to be $2\%$, or $0.02$. Substituting these values into the decreasing exponential function yields $f(x)=3,000(1-0.02{)}^x$, which is equivalent to $f(x)=3,000(0.98{)}^x$.