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

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

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,

`=(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

`=(16-256)/(5-1)`

`=(-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.