Question

a checkers tournament starts with 2048 players. after each round, a quarter of the players are eliminated. write an equation that represents the number of players, p, that remain after r rounds. how many players will be remaining after three rounds? p = 2048(0.25)^r there will be 32 players left after three rounds p = 2048(0.75)^r there will be 864 players left after three rounds p = 2048(0.25r) there will be 1536 players left after three rounds p = 2048/r there will be 683 players left after three rounds

Explanation:

Step1: Determine the remaining - fraction

Since a quarter ($0.25$) of the players are eliminated each round, the fraction of players that remain each round is $1 - 0.25=0.75$.

Step2: Write the general - equation

The initial number of players is $2048$. After $r$ rounds, the number of remaining players $P$ follows an exponential - decay model: $P = 2048(0.75)^{r}$.

Step3: Calculate the number of remaining players after 3 rounds

Substitute $r = 3$ into the equation $P = 2048(0.75)^{r}$.
$P=2048\times(0.75)^{3}=2048\times\frac{3}{4}\times\frac{3}{4}\times\frac{3}{4}=2048\times\frac{27}{64}=864$.

Answer:

B. $P = 2048(0.75)^{r}$, There will be 864 players left after three rounds