Question

the nba invited 128 teams to compete in a tournament.after each round,half of the team were eliminated which equation represents the number of teams,that remained in the tournament after,r, rounds

Answer 1

The equation that represents the number of teams remaining in the tournament after each round is: Remaining teams = 128 * (1/2)^(r), where r is the number of rounds completed.

Step-by-step explanation:

The number of teams that remain in the tournament after each round can be represented by the equation:

Remaining teams = 128 * (1/2)^(r)

Where r is the number of rounds completed. Each round halves the number of teams remaining, so the remaining teams can be calculated by multiplying the initial number of teams (128) by 1/2 raised to the power of the number of rounds.

Answer 2

Tr = 128(1/2)^r

Step-by-step explanation:

After round 1, half of 128 is eliminated = 128/2 = 64

After round 2, half of 64 is eliminated = 64/32 = 32

After round 3, half of 32 is eliminated = 32/2 = 16

After round four, half of 16 is eliminated which is 16/2 = 8

Now, the pattern we have is;

128, 64, 32, 16, 8

The succeeding term keeps decreasing by 2 compared to the preceding term

We can see that this is a geometric pattern with a = 128 and r = 1/2

The nth term is thus

Tn = 128 * (1/2)^n

Thus, the number of teams remaining after r round would be

Tr = 128 * (1/2)^r