Church youth group math question

Discussion in 'Secondary Education' started by 1cubsfan, May 31, 2012.

  1. 1cubsfan

    1cubsfan Companion

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    May 31, 2012

    I have a question that I would like to pose to a church youth group, but it involves math. I have a rudimentary understanding of how to figure out the problem (English teacher here!), but don't fully understand the math behind it. Here is the scenario:

    Suppose all 10 of you decided to convert 5 people to our faith, and committed to walking with these people for 5 years in order to help them grow. After 5 years, if each of you worked for 5 converts, there would be 50 new members of the faith. After those 5 years, suppose all of those 50 people took 5 people and over the course of 5 years led those people to the faith. And then those 250 people.... And so on and so on.

    After 50 years, how many people would be converted to the faith?
    How long would it take for the entire world to be converted to the faith?

    So I was wondering if you could tell me if these are questions high schoolers will be able to answer, and if they have trouble getting started, what is a good hint I can give them to get them started in the right direction?

    Thanks!
     
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  3. Aliceacc

    Aliceacc Multitudinous

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    May 31, 2012

    They could do it by straight arithmetic: set up a chart, figure out each year's total.

    If they choose to do it more mathematically, it's not a difficult problem-- if you know the formulas. (Our kids see it Junior Year.) It's called a Geometric Sequence, and they want to find the General Term. In this particular case, a1 (the first number) is 50, n=10 (since there are 10 increments to get you to that 50 year mark-- the fact that each one takes 5 years is immaterial as far as the math goes) and r (the number you're multiplying by each time) is 5.

    It's going to be a BIG number... warn them that a typical scientific calculator may have to round it off using scientific notation.

    Sorry, I don't have my calculator here and I'm in the middle of schoolwork.
     
  4. jwteacher

    jwteacher Cohort

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    May 31, 2012

    Since Alice beat me to it, the answer is 97,656,250.
     
  5. Aliceacc

    Aliceacc Multitudinous

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    May 31, 2012

    Oops, I realized I never gave you the formula--- sorry:

    x = a1*r ^(n-1)
    or 50(5^10 - 1)
    or 50( 5 ^ 9)

    Remind them to raise 5 to the 9th BEFORE they multiply it by 50-- its' called Order of Operations.
     
  6. 1cubsfan

    1cubsfan Companion

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    Thanks!
     
  7. Aliceacc

    Aliceacc Multitudinous

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    You're welcome! I love this stuff!
     
  8. czacza

    czacza Multitudinous

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    Jun 1, 2012

    1cubs...are you goingto be able to help the kids who don't understand the math behind this?
     
  9. HMM

    HMM Cohort

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    Am I missing something...Don't we need to add them all up


    after the first 5 years we have 50 new people converted

    then those 50 people convert 250 new people...so at this point we have 50+250=300 people converted since the beginning of this process...and so on.
     
  10. CindyBlue

    CindyBlue Cohort

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    I had a long answer posted here, using the geometric series formula...think I might need geometric sequence...with series, I got S(sub 11) = 122,070,310, then thought I should subtract out the original 10 people, so that would make 122,070,300. But should I have used the geometric sequence formula instead?
    (Edited to fix division error!)
     
  11. Aliceacc

    Aliceacc Multitudinous

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    Inexcusably careless mistake... sorry about that.

    The correct formula is:
    [a1(1-r^n)] / (1-r)

    It's the formula for the sum of the terms of a geometric sequence.

    I get 122,070,300.

    Now, given my litany of excuses- still recovering from last weekend, the insanity that IS NHS for graduation Sunday, would someone please check my math??
     
  12. CindyBlue

    CindyBlue Cohort

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    Thanks...I fixed my division error (I put 11 in for r in the denominator - grrr!)


     
  13. HMM

    HMM Cohort

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    Jun 1, 2012

    That is what I get
     
  14. Aliceacc

    Aliceacc Multitudinous

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    Thank you!
     

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