Question

1. A tennis tournament starts with 120 players. During each round of the game, half of the players are eliminated from the tournament. What kind of function best models the relationship between the number of players in the tournament, y, and the game round, x?

Answer 1

Answer:

Exponential function; $y=120(\frac{1}{2})^x$.

Step-by-step explanation:

We have been given that a tennis tournament starts with 120 players. During each round of the game, half of the players are eliminated from the tournament.

We can see that the change in number of eliminated players is not constant. The number of players in tournament is decreasing exponentially. Therefore, an exponential function best models the relationship between the number of players in the tournament, y, and the game round, x.

We know that exponential decay function is in form $y=a(b)^x$, where,

y = Final amount,

a = Initial amount,

b = Decay factor,

t = Time

Since during each round of the game, half of the players are eliminated from the tournament, so decay factor would be $\frac{1}{2}$.

Initially there were 120 players, so $a=120$.

Therefore, our required equation would be $y=120(\frac{1}{2})^x$.