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?

Answer 1

Given that there are 128 teams in a softball tournament and in each round half of the teams are eliminated, the number of teams remaining after each round can be modeled using an exponential decay function.

Initially, there are 128 teams. After 1 round, the number of teams is halved, so 64 teams remain. After 2 rounds, another half of the teams are eliminated, leaving 32 teams, and so on.

The number of teams remaining after \( x \) rounds can be described by the function:
\[ T(x) = \frac{128}{2^x} \]

Alternatively, this can be written using exponents as:
\[ T(x) = 128 \cdot \left(\frac{1}{2}\right)^x \]
or equivalently:
\[ T(x) = 128 \cdot 2^{-x} \]

Where \( T(x) \) is the number of teams remaining after \( x \) rounds.