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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 :

MRROYALGO

Answer:

It can not be modeled by a linear function

Step-by-step explanation:

The given parameters can be represented as:

[tex](x_1,y_1) = (1,64)[/tex]

[tex](x_2,y_2) = (2,32)[/tex]

[tex](x_3,y_3) = (3,16)[/tex]

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)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

and

[tex]m = \frac{y_3 - y_2}{x_3 - x_2}[/tex]

Using: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex], we have:

[tex]m = \frac{32 - 64}{2 - 1}[/tex]

[tex]m = \frac{-32}{ 1}[/tex]

[tex]m = -32[/tex]

Using [tex]m = \frac{y_3 - y_2}{x_3 - x_2}[/tex], we have:

[tex]m = \frac{16 - 32}{3 - 2}[/tex]

[tex]m = \frac{-16}{1}[/tex]

[tex]m = -16[/tex]

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

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