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. How does an exponential function describe tournament play? Include the following in your answer: - an explanation of how you could use y=2x to determine the number of rounds for 128 teams, and - an explanation of an inappropriate number of teams for tournament play with an explanation of why this number would be inappropriate.

Answer 1

In an exponential function like y = 2^x, the base is constant and the exponent is the variable.

y signifies the number of teams required 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 natural logarith or ln of both sides:ln(128) = x(ln(2)) x = ln(128) / ln(2) x = 7 So there will be 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:

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

Answer 2

In an exponential function like y = 2^x, the base is constant and the exponent is the variable.

y signifies the number of teams required 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 natural logarith or ln of both sides:ln(128) = x(ln(2)) x = ln(128) / ln(2) x = 7 So there will be 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:

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