The NCAA Basketball Championship (also known as March Madness) is an example of exponential decay. At each round of the tournament, teams play against one another with only the winning teams progressing to the next round. In other words, the number of teams playing at each round is half of the number of teams playing in the previous round. The equation f(x)= 64(0.50)x

Question

represents the pattern in this situation. Define an appropriate range for this situation.

(1 point)
Responses

1 ≤ x ≤ 64
1 ≤ x ≤ 64

1 ≤ y ≤ 64
1 ≤ y ≤ 64

64 ≤ y ≤ 1
64 ≤ y ≤ 1

64 ≤ x ≤ 1

Answer 1

In the context of the NCAA Basketball Championship, the variable \( x \) represents the number of rounds in the tournament, while \( y \) represents the number of teams remaining after each round.

The tournament starts with 64 teams, and in each round, half of the teams are eliminated. Therefore, after each round, the number of teams can be represented by the function \( f(x) = 64(0.50)^x \).

To define an appropriate range for this situation:

• The value of \( x \) (the number of rounds) will start at 0 (the initial state with 64 teams) and can go up to a maximum of 6 rounds (the tournament concludes with a single champion). Thus, the range for \( x \) is: \[ 0 \leq x \leq 6 \]

• The value of \( y \) (the number of teams remaining) starts at 64 and decreases towards 1 as the rounds progress. Thus, the range for \( y \) is: \[ 1 \leq y \leq 64 \]

Given the options you provided, the most appropriate response for the range of \( y \) is: \[ 1 \leq y \leq 64 \]