Question

There are a total of 128 teams at the start of the citywide 3 on 3 basketball tournament. half the teams are eliminated after each round. write and solve an exponential equation to determine after which round there are 16 left

Answer 1

Let T be the number of teams after n rounds.
$T=128\times(\frac{1}{2})^{n}$

When T = 16, we get:$16=128\times(\frac{1}{2})^{n}$
Dividing both sides by 128, we get:
$\frac{1}{8}=(\frac{1}{2})^{n}$
Therefore n = 3
The answer is 'after the third round'.