Homework Help: Algebra

Posted by Renee on Wednesday, March 10, 2010 at 1:10am.

How do you find the function to a problem quickly?

For example: A tennis club holds a doubles tournament every spring. This year the club has 40 teams involved. At the end of each round half of the teams are eliminated. How many rounds must be played to determine the winner?

So, I already found the answer (6 rounds). How do I find its function or equation to solve?

Algebra - scott, Wednesday, March 10, 2010 at 1:15am
wouldn't it just be 40^1/2 that's 6.32 so 6 rounds
Algebra - Renee, Wednesday, March 10, 2010 at 1:21am
But...
The table is like this
x=Number of the round
y=Teams in the round

X Y
1 40
2 20
3 10
4 5
5 2.5
6 1.25 -> 1

How do I find the function or equation using variables x and y?
(To find the function more faster because, I have 3 other problems like this and I want to try to do the others on my own.)
Algebra - scott, Wednesday, March 10, 2010 at 1:23am
Well This is what I did to get 40^.5 you know the amount Y and then you already know the function X its Y^x.
that's what I just went over today in class
Algebra - drwls, Wednesday, March 10, 2010 at 1:24am
The number of rounds is the smallest integer n that satisfies
N*(1/2)^n = 1
where N is the number of teams.
for n = 5, 40*(1/2)^5 = 1.25
for n = 6, 40*(1/2)^6 = 0.625
So n is the answer.

It has nothing to do with square roots, as the previous answer suggests.
Algebra - Renee, Wednesday, March 10, 2010 at 1:27am
Thanks! (;
Algebra - drwls, Wednesday, March 10, 2010 at 1:29am
n=6 rounds are needed, including the championship. With 40 teams, there can be a lot of "byes" in early rounds. Up to 64 teams could be included in a 6-round tournament.
Algebra - Renee, Wednesday, March 10, 2010 at 1:31am
Also how did u find its function easily? Everytime I try to find the function it takes me a super long smount of time.
Algebra - rachaekl, Monday, April 8, 2013 at 11:05am
what is the surface area of a rectangular prism with a base area 15m2, height 3m, and lateral area 18m2?? This is my question !!! PLEAS ANSWER

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