SAT Question ffdfe1e1: Nonlinear Functions answer and explanation with Desmos solution

Choice C is correct. It’s given that one of the two players in a match is eliminated during each round. Therefore, the number of players decreases by half at the end of each round, and so the number of players eliminated at the end of a round also decreases by half. A decreasing exponential equation can be written in the form $p=a(1-b{)}^r$, where $b$ is the value of the decrease each round, $r$, and $a$ is the value of $p$, the number of players, when $r=0$. It's given that there are $240$ players in the tennis competition. Therefore, $a=240$. Since the number of players eliminated at the end of a round decreases by half, it follows that $b=\frac{1}{2}$. Substituting $240$ for $a$ and $\frac{1}{2}$ for $b$ in the equation $p=a(1-b{)}^r$ yields $p=240(1-\frac{1}{2}{)}^r$, or $p=240(\frac{1}{2}{)}^r$.