I had to do an experiment where I started with 30 coins, tossed them onto a tabl

Question

I had to do an experiment where I started with 30 coins, tossed them onto a table and removed the ones that landed face up. I kept doing this until I had none left. I kept a table of the results:

Toss        # of Coins remaining 0                  30 1                  16 2                  7 3                  1 4                  1 5                  1 6                  1 7                  0 I had to come up with an equation that would best fit this, and I came up with: C(n)=C(0) (1/2)^n , where C(n) is the # of coins at toss, C(0) is initial number of coins, and n is the number of the toss. This is modeled after exponential decay. The part that I am having a problem with is now that it's asking me to "State the equation that would predict the number of remaining coins if you began with N(0) coins." I will rate well! :) I had to do an experiment where I started with 30 coins, tossed them onto a table and removed the ones that landed face up. I kept doing this until I had none left. I kept a table of the results:

Toss        # of Coins remaining 0                  30 1                  16 2                  7 3                  1 4                  1 5                  1 6                  1 7                  0 I had to come up with an equation that would best fit this, and I came up with: C(n)=C(0) (1/2)^n , where C(n) is the # of coins at toss, C(0) is initial number of coins, and n is the number of the toss. This is modeled after exponential decay. The part that I am having a problem with is now that it's asking me to "State the equation that would predict the number of remaining coins if you began with N(0) coins." I will rate well! :) I will rate well! :)

Explanation / Answer

The equation that you came up with C(n)=C(0) * (1/2)^n actually is exactly the equation you are looking for for your question. When you interpreted the equation you assumed at C(n) was the # of coins tosses which is incorrect. In the said equation C(n) is actually the number of coins remaining. the n variable is the # of tosses. So the formula actually reads remaining coins (C(n))= Initial coins (C(0)) * (1/2)^number of trials (n). Therefore the equation you want is N(n)= N(0)+(1/2)^n if you want it terms of N.

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