Question

a large chess tournament starts with 1024 players. after each round, half of the players are eliminated.
part a:
write an equation that represents the number of players, p, that remain after r rounds, and explain how you determined your answer.
part b:
how many players will there be remaining after 6 rounds?

Explanation:

Step1: Identify the pattern

The initial number of players is 1024 and it is halved each round. So the general formula for exponential - decay is $P = P_0\times(\frac{1}{2})^r$, where $P_0$ is the initial number of players and $r$ is the number of rounds. Here, $P_0 = 1024$. So the equation is $P=1024\times(\frac{1}{2})^r$.

Step2: Substitute values for part B

We want to find the number of players after 6 rounds. Substitute $r = 6$ into the equation $P = 1024\times(\frac{1}{2})^r$. First, calculate $(\frac{1}{2})^6=\frac{1}{64}$. Then, $P = 1024\times\frac{1}{64}$. Since $1024\div64 = 16$, so $P = 16$.

Answer:

Part A: The equation is $P = 1024\times(\frac{1}{2})^r$ because the number of players is halved each round starting from 1024.
Part B: 16