Question

There is a state soccer tournament with 128 teams competing for 1st place. Each week, half of the teams get eliminated. How many teams remain after 6 weeks?

A.
16
B.
8
C.
4
D.
2

Answer 1

`\text{Let A denote the number of teams after n weeks}`


`A_0 = 128`

`A_1 = A_0(0.5) = 128(0.5)`

`A_2 = A_1(0.5) = 128(0.5)^(2)`

`A_3 = A_2(0.5) = 128(0.5)^(3)`


`A_n = 128(0.5)^(n)`

`A_6 = 128(0.5)^(6) = 2`

Thus, after 6 weeks, there will only be 2 teams left.

Answer 2

The answer is D.
Week 0 (start; initial): 128 TEAMS
Week 1: 64 teams
Week 2: 32 teams
Week 3: 16 teams
Week 4: 8 teams
Week 5: 4 teams
Week 6: 2 teams

You can also solve for this using a common ratio.