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there's this question I am working on and I am mostly through it (well, I hope I am at least), there's just one or two things still annoying me/need confirmation.

Here's the question: 50 coins were flipped. For every coin that landed with the head showing upwards, it was taken away. The remaining amount that landed on tails side up were flip again. This process happened repeatedly until all the coins were taken away. The results are below.

flips: 1 2 3 4 5 6 7

amount remaining: 22 7 2 1 1 1 0

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So, when flips = 0, amount remaining = 50

basically, I can see that it is exponential (I can also prove mathimatically that it isn't linear), I can plot it and show that its exponential but my maths is a bit rough trying to prove it being exponential.

I know i can use the formula b = (y2/y1)^(1/x2-x1) for the separate values of the table to prove that it is exponential. For a perfect expoential, they would all be the same but mine are slightly out (some more so at different places). Do you think it would still be acceptable to so that its only up to chance (50/50) for the coin to land in the same place and its only a slight varience in chance that leads to it not being a perfect exponential function?

The next problem is my function for this data. Following the formula for a above, I guess I would do an average of all the b's to find the b for the function y = ab^x ?

then I just add the a value of 50 to get y = 50b(the average of all the b's)^x

does that seem right?

are there any flaws in my reasoning?

Thank-you very much!