My Math Forum What formula for this exponentially decreasing set of data?

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 November 9th, 2015, 11:39 AM #1 Newbie   Joined: Nov 2015 From: Miami Posts: 2 Thanks: 0 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?
 November 9th, 2015, 12:55 PM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 3,044 Thanks: 1627 0.5 should have 21.25 as its function value $y = 20+40 \cdot 2^{-10x}$ Thanks from alex11111
 November 9th, 2015, 12:56 PM #3 Senior Member     Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 $\displaystyle 40-10\cdot\frac{1-(\frac{1}{2})^{n-1}}{1-\frac{1}{2}}$ n=1,2,3,... Thanks from alex11111
November 9th, 2015, 06:03 PM   #4
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Quote:
 Originally Posted by skaa $\displaystyle 40-10\cdot\frac{1-(\frac{1}{2})^{n-1}}{1-\frac{1}{2}}$ 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.

November 10th, 2015, 05:18 AM   #5
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From: Chicago, IL

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Quote:
 Originally Posted by alex11111 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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