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Math Help - Exponential Functions-Word Problem: Predicting an Exponential Formula

  1. #1
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    Exponential Functions-Word Problem: Predicting an Exponential Formula

    I tried to solve this for over two hours without any successful results.
    If you could please provide the solution and explain how you arrived at it, it would be very much appreciated. I am perplexed at this point.
    --
    An experiment with coins is performed. The experimenter starts with 4 coins. Each time she tosses the coins into the air, after they land, she counts the number of heads that appear and adds that amount (the number of heads) of coins to what she previously had. (i.e she tosses 4 coins, 2 out of 4 are heads, 4+2=she now has six coins.)

    The experimenter repeats this process and claims that one could make a rough prediction about how the coins will increase (given any amount of tosses) based on the formula for compound interest: A=P(1+ i)n


    Of course:
    In this case, P represents the amount of coins she started with.
    i = 0.5 since the 50% probability of the coins landing on heads.
    n= the number of tosses

    If her her hypothesis is correct, create a formula that predicts the total number of coins if an unfair coin is used (a weighted coin included in her starting amount of 4) that only comes up heads 1 out of every 4 times.

    Thanks in advance.

    Sincerely,

    Raymond
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  2. #2
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by raymac62 View Post
    I tried to solve this for over two hours without any successful results.
    If you could please provide the solution and explain how you arrived at it, it would be very much appreciated. I am perplexed at this point.
    --
    An experiment with coins is performed. The experimenter starts with 4 coins. Each time she tosses the coins into the air, after they land, she counts the number of heads that appear and adds that amount (the number of heads) of coins to what she previously had. (i.e she tosses 4 coins, 2 out of 4 are heads, 4+2=she now has six coins.)

    The experimenter repeats this process and claims that one could make a rough prediction about how the coins will increase (given any amount of tosses) based on the formula for compound interest: A=P(1+ i)n


    Of course:
    In this case, P represents the amount of coins she started with.
    i = 0.5 since the 50% probability of the coins landing on heads.
    n= the number of tosses

    If her her hypothesis is correct, create a formula that predicts the total number of coins if an unfair coin is used (a weighted coin included in her starting amount of 4) that only comes up heads 1 out of every 4 times.

    Thanks in advance.

    Sincerely,

    Raymond
    If a_{n} is the number of coins after n tosses and p is the 'probability of head' , the approximative increment is the solution to the difference equation...

    a_{n+1}= a_{n}\ (1+p) (1)

    ... and it is given by...

    a_{n}= a_{0}\ (1+p)^{n} (2)

    ... where a_{0} is the initial number of coins [in your case 4...]. That under the hypothesis that all the available coins are tossed each time...

    Kind regards

    \chi \sigma
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  3. #3
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    Quote Originally Posted by chisigma View Post
    If a_{n} is the number of coins after n tosses and p is the 'probability of head' , the approximative increment is the solution to the difference equation...

    a_{n+1}= a_{n}\ (1+p) (1)

    ... and it is given by...

    a_{n}= a_{0}\ (1+p)^{n} (2)

    ... where a_{0} is the initial number of coins [in your case 4...]. That under the hypothesis that all the available coins are tossed each time...

    Kind regards

    \chi \sigma
    I knew the formula for compound interest.

    I forgot to raise the the  n in the equation of my original post.

    Would P=3.25 represent starting with a weighted coin that only landed on heads 1/4 of the time? Where  "P" represents the variable indicated in my original post. (The initial amount of coins.)

    Thanks in advance.

    Sincerely,

    Ray
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