Question

Mason is one of 320 players participating in an online tournament. After each round of play, half of the players are eliminated. Mason hopes to remain in the tournament through the fourth round. Determine how many players will be left in the tournament after the 4th round.

Answer 1

20 Players

Explanation:

The number of players remaining decreases by half with each round played. This can be represented by a 50% decrease in the number of players per round, which means that this is an exponential decay situation.

The number of players remaining after x rounds can be represented by an exponential expression, a(b)x, where a represents the initial number of players, b represents the growth or decay factor, and x represents the number of rounds. Determine b by solving the formula, b = 1 - r, when r = 0.50.

`b= 1 - r\\b= 1 - 0.50\\b= 0.50`

It is given that a = 320 and x = 4. Substitute these values along with b = 0.50 into the general exponential expression.

`320(0.50)^4`

Let y represent the number of players remaining after 4 rounds. Set this equal to the expression representing the number of players after 4 rounds and evaluate for y.

`y= 320(0.50)^4\\y= 320(0.625)\\y= 20`

Therefore, after 4 rounds, there will be 20 players remaining in the tournament.

Answer 2

320/2 = 160
160/2 = 80
80/2 = 40
40/2 = 20

There are going to be 40 players in the 4th round, and 20 left AFTER the 4th round


hoope this helps