Question

A chess competition has eliminations each round. The table below shows the number of players in each of the first 5 rounds of the tournament:

Round (x)
12345

Players f(x)
256128643216

Compute the average rate of change of f(x) from x = 1 to x = 5 and identify the meaning of that rate.

A.) −60; on average, there was a loss of 60 each round.
B.) −240; on average, there was a loss of 240 each round.
C.) 4; there were 4 rounds between rounds 1 and 5.
D.) 240; there were 240 fewer players between rounds 1 and 5.

Answer 1

Round    (x) 1      2     3    4   5
Players f(x) 256  128  64  32  16

16-256 / 5 - 1 = -240/4 = -60

A.) −60; on average, there was a loss of 60 each round. 

Answer 2

Answer:

A. −60; on average, there was a loss of 60 each round.

Step-by-step explanation:

A chess competition has eliminations each round. The table that shows the number of players is,

Round   (x)        1         2     3    4    5

Players f(x)       256  128  64  32  16

The average rate of change of f(x) from x₁, x₂ is,

$=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}$

Here, we have to calculate the average rate of change of f(x) from x = 1 to x = 5, so it will be

$=\dfrac{16-256}{5-1}$

$=\dfrac{-240}{4}$

$=-60$

As the number of players getting decreased, so the rate will be in negative. As the rate was found to be -60, so it means in each round on an average 60 players are getting eliminated.