There are 128 teams in a softball tournament. In each round, half of the teams are eliminated. Which function can be used to find the number of teams remaining in the tournament after `x` rounds?

Question

a. y=128\left(2\right)^{x}
b. y=0.5\left(128\right)^{x}
c. y=128\left(0.5\right)^{x}
d. =128^{x}

Answer 1

To determine the function that represents the number of teams remaining in the tournament after \( x \) rounds, we need to understand the elimination process.

Starting with 128 teams, in each round half of the teams are eliminated. This means that after each round, the number of teams is halved.

After \( x \) rounds, the number of remaining teams can be calculated as:

1. Start with 128 teams.
2. After 1 round: \( 128 \times 0.5 \)
3. After 2 rounds: \( 128 \times 0.5^2 \)
4. After 3 rounds: \( 128 \times 0.5^3 \)
5. After \( x \) rounds: \( 128 \times 0.5^x \)

Putting it all together, the number of teams remaining after \( x \) rounds can be expressed as:

\[ y = 128 \times (0.5)^x \]

Thus, the correct function is:

c. \( y = 128(0.5)^{x} \)