J.R. S. answered • 10/05/17

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If you recover 50% each time you do an extraction, then after the 1st extraction you have 50%

After the 2nd, you have 50% of the remaining 50%, or another 25% for a total of 75%. Etc., etc.

The formula for such an event is fraction remaining = 0.5

^{n }where n is the number of extractions.For 98% extraction, that would leave 2% as fraction remaining = 0.02

0.02 = 0.5

^{n}log 0.02 = n log 0.5

-1.699 = -0.301 n

n = 5.6, so you would need to do 6 extractions.

Looking at it the long way

extraction # amount recoverd

1..................50%

2.................25%

3.................12.5%

4.................6.25%

5................3.125%

6................1.563%

Add them all up to get 98.4%