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
teams left after 1 week = 64 = 128(1/2)
teams left after 2 weeks = 32 = 128(1/2)^2
..
teams left after 6 weeks = 128(1/2)6 = 2
To find out how many teams remain after 6 weeks, we need to keep halving the number of teams each week. We start with 128 teams and halve that number each week.
Week 1: 128 ÷ 2 = 64 teams remaining
Week 2: 64 ÷ 2 = 32 teams remaining
Week 3: 32 ÷ 2 = 16 teams remaining
Week 4: 16 ÷ 2 = 8 teams remaining
Week 5: 8 ÷ 2 = 4 teams remaining
Week 6: 4 ÷ 2 = 2 teams remaining
So, after 6 weeks, only 2 teams remain. Therefore, the answer is D. 2.