Question

Round 1 of a tennis tournament starts with 64 players. After each round, half of the players have lost and are eliminated from the tournament. Therefore, in round 2 there are 32 and in round 3 there are 16 players and so on. Can this relationship be modeled by a linear function? Provide evidence to support your claim.

Answer 1

Answer:

It can not be modeled by a linear function

Step-by-step explanation:

The given parameters can be represented as:

$(x_1,y_1) = (1,64)$

$(x_2,y_2) = (2,32)$

$(x_3,y_3) = (3,16)$

Where: x = rounds and y = players

Required:

Determine if it can be represented by a linear function

To do this, we simply calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

and

$m = \frac{y_3 - y_2}{x_3 - x_2}$

Using: $m = \frac{y_2 - y_1}{x_2 - x_1}$, we have:

$m = \frac{32 - 64}{2 - 1}$

$m = \frac{-32}{ 1}$

$m = -32$

Using $m = \frac{y_3 - y_2}{x_3 - x_2}$, we have:

$m = \frac{16 - 32}{3 - 2}$

$m = \frac{-16}{1}$

$m = -16$

Since both slopes are not the same, the relationship be modeled by a linear function