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November 9th, 2015, 11:39 AM   #1
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What formula for this exponentially decreasing set of data?

I have this set of data:

0.1 || 40
0.2 || 30
0.3 || 25
0.4 || 22.5
0.5 || 21.75

As you can see it decrease by half of the previous increment. How can I put that as a formula?

I tried something along the lines of:

40 - 10*(x-1)/2ˆx
but it's not right.

How can I correct that formula?
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November 9th, 2015, 12:55 PM   #2
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0.5 should have 21.25 as its function value

$y = 20+40 \cdot 2^{-10x}$
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November 9th, 2015, 12:56 PM   #3
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$\displaystyle 40-10\cdot\frac{1-(\frac{1}{2})^{n-1}}{1-\frac{1}{2}}$
n=1,2,3,...
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November 9th, 2015, 06:03 PM   #4
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Quote:
Originally Posted by skaa View Post
$\displaystyle 40-10\cdot\frac{1-(\frac{1}{2})^{n-1}}{1-\frac{1}{2}}$
n=1,2,3,...
Thanks for your response. Is your formula equivalent to skeeter's? His formula seems to work but can't work out the difference with yours.
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November 10th, 2015, 05:18 AM   #5
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Quote:
Originally Posted by alex11111 View Post
Is your formula equivalent to skeeter's?
His formula works for x=0.1, 0.2, 0.3,... , my formula for n=1, 2, 3,... . No more differences.
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