Algebra

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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 -

    wouldn't it just be 40^1/2 that's 6.32 so 6 rounds

  • Algebra -

    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 -

    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 -

    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 -

    Thanks! (;

  • Algebra -

    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 -

    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 -

    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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