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Math Help - Coins Question..

  1. #1
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    Coins Question..

    I figured a picture would better describe the problem.

    The Lesson I was working on was Transformations of Logarithmic Equations.
    Then all of a sudden this questions comes up?
    I did the experiment and figured the Toss would equal x, and the Coins would equal y. Then graphed it. Although there's no need to use an xy graph I figured, it's only what we've been working on this whole entire time.

    I can't say for sure what equation to use, since the amount of remaining coins after each toss is not a constant.
    It sort of resembles this kind of graph, but transformed and no asymptote.
    y=(1/2)^x

    Other than that, I have no idea on what the equation should be.
    y=20(1/2)^{n} , representing half-Life phenomenon?




    Last edited by NotSoBasic; June 6th 2009 at 07:47 PM.
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  2. #2
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    Coin tossing experiment

    Hello NotSoBasic

    I reckon you have got this pretty well correct! If you repeat the whole experiment a large number of times, and average the results at each stage, you would expect the number of coins left to be halved after each toss. So, if you start with 20 coins, and there are y coins left after n tosses, y = 20 (\tfrac12)^n is the equation that will model this situation.

    Grandad
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  3. #3
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    Thanks!
    The equation does make more sense if you repeat it and take the averages.
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    PartC) State the equation that would predict the number of remaining coins if you began with N_0 coins..

    Assuming N_0 means any number to start.

    For example, if I started with 10 coins, and tossed them, then I would end up with ~5 coins.

    So, N_0 (\tfrac 12)
    However, it graphs as a horizontal line @ y-intercept 5.
    But that would be the answer.
    Any thoughts?
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  5. #5
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    Sorry guys I've been working on these two experiments for hours!
    It's not like me to ask so much, but if anyone has the time to review these questions with me, it would be much appreciated, I have no one else to turn too.




    The brackets represent the actual answer. It said to use the same coins (20) from previous question.



    PartB) Equation might be y=2^n+3
    (0,4) is the starting point, since I decided to start with 4 coins.
    The equation seems to make sense until about toss 6/7, where it starts to double. The thing is while performing the experiment, it should be about 1/2 added to previous number, not doubling.

    PartC) Here, I understand the answer might be. N_0(\tfrac 12)+N_0=y
    Meaning, whatever number I start with, after the toss, would result in 1/2 and I would add that to the number of coins I started with.
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    Coin tossing experiment

    Hello NotSoBasic

    Here's the theoretical answer, if you average the results over a large number of experiments.

    Starting with N_0 coins, then on the first toss you would expect (in the long run) \tfrac12N_0 to land heads. So when this number is added to the original N_0 coins you would have N_0+\tfrac12N_0=\tfrac32N_0 coins in total.

    So when n =1, y =\tfrac32N_0

    On the next toss, you'd expect half of this new number to land heads: that's \tfrac12.\tfrac32N_0. Adding these to the number you had makes \tfrac32N_0+\tfrac12.\tfrac32N_0=\tfrac32N_0(1+\tf  rac12)=(\tfrac32)^2N_0

    So when n =2, y =(\tfrac32)^2N_0

    You'll see that the expected number after each throw is \tfrac32 times the number at the beginning of the throw.

    So after n throws, you would expect y = (\tfrac32)^nN_0 coins. That's the equation that would predict the number of coins.

    Grandad
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  7. #7
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    You are...AMAZING!

    Thanks so much for taking the time to teach me how to do these problems.
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  8. #8
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    I'm still having problems trying to figure out what equation would work best to represent the graph in question 23.

    y=2^x+3 is not the correct equation..

    I'm thinking, y=4(\tfrac 32)^n
    Last edited by NotSoBasic; June 15th 2009 at 06:02 PM.
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    Coin tossing experiment

    Hello NotSoBasic
    Quote Originally Posted by NotSoBasic View Post
    I'm still having problems trying to figure out what equation would work best to represent the graph in question 23.

    y=2^x+3 is not the correct equation..

    I'm thinking, y=4(\tfrac 32)^n
    That's correct. If you start with 4 coins, the predicted number after n tosses is 4(\tfrac 32)^n.

    Grandad
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  10. #10
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    Thanks again Grandad!
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