The number of teams remaining in a tournament decreases as each round of the tournament is completed. The function below models the total number of teams remaining after x rounds. Which statement about the function is true?

Question

T(x) = 256(1-b)x

(1 point)
Responses

The number 256 represents the decay rate of the function.
The number 256 represents the decay rate of the function.

The number 256 represents the growth rate of the function.
The number 256 represents the growth rate of the function.

The espression 1-b represents the decay rate of the function.
The espression 1-b represents the decay rate of the function.

The expression 1- b represents the growth rate of the function.

Answer 1

To analyze the function \( T(x) = 256(1-b)^x \):

1. Identify the components of the function:

   • The number 256 is the initial value, representing the total number of teams at the start (before any rounds are completed).
   • The term \( (1-b)^x \) represents how the number of teams decreases over rounds. The expression \( 1-b \) is a fraction (between 0 and 1) if \( b \) is a positive number less than 1, which indicates a decay or decrease as \( x \) increases.

2. Determine the meaning of the parameters:

   • The number 256 does not represent a decay or growth rate; it indicates the initial amount of teams.
   • The expression \( 1-b \) indicates how the teams decay with each round because it reduces the total teams remaining as \( x \) increases.

Thus, the correct statement is:

The expression \( 1-b \) represents the decay rate of the function.