Question

Each year, the local country club sponsors a tennis tournament. The tournament starts with 128 participants. During each round, half of the players are eliminated. Create a function to represent the number of players in the tournament.

Fill in the values of 'a' and 'b' to complete the function:
A) a = 128, b = 1/2
B) a = 1, b = 2
C) a = 2, b = 1
D) a = 1/2, b = 128

Answer 1

The function to represent the number of players remaining in each round of the tournament is f(x) = 128 × (1/2)^x, making the correct answer A) a = 128, b = 1/2.

Step-by-step explanation:

The student has asked to create a function to represent the number of players in a tennis tournament that starts with 128 participants and eliminates half of the players each round. The correct function would have the initial number of participants (128) decrease by a factor of one half with each subsequent round. A function that models this situation is f(x) = a × (b)^x, where a represents the initial number of participants and b represents the fraction of players remaining after each round. The number of rounds is represented by x.

Therefore, the values for 'a' and 'b' that complete the function are:

• a = 128, because that is the initial number of participants.
• b = 1/2, because after each round, half of the players are eliminated.

So, the answer is A) a = 128, b = 1/2.