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
Let T be the number of teams after n rounds. [tex]T=128\times(\frac{1}{2})^{n}[/tex]
When T = 16, we get:[tex]16=128\times(\frac{1}{2})^{n}[/tex] Dividing both sides by 128, we get: [tex]\frac{1}{8}=(\frac{1}{2})^{n}[/tex] Therefore n = 3 The answer is 'after the third round'.
