Question

The NCAA basketball tournament begins with 64 teams and consists of 6 rounds of play. The winners of the first round play against each other in the second round. The winners then move from the Sweet Sixteen to the Elite Eight to the Final Four and finally to the Championship Game.
The number of teams y that compete in a tournament of x rounds is y=2^x
How does an exponential function describe tournament play ?
Include the following in your answer:
an explanation of how you could use y=2^x to determine the number of rounds for 128 teams, and an example of an inappropriate number teams...

Answer 1

tournament play with an explanation of as why this number would be inappropriate.

Answer 2

@memecheaa @mrnood

Answer 3

y represents the number of teams needed for x rounds. So if you only have 1 round, you need 2 teams because 2^1 = 2.

Sub in 128 for y:

128 = 2^x

Take the ln of both sides

ln(128) = x(ln(2))
x = ln(128) / ln(2)
x = 7

So you would need 7 rounds.

An inappropriate number of teams would be any odd number because this would result in a decimal amount of rounds, which makes no sense. Say you had 5 teams

5 = 2^x
x = ln(5) / ln(2)
x = 2.32

Also, 0 teams would be inappropriate, because then there would be no tournament :P