Math Problem.....

[markjs]

If I have a bottle of solution with six parts of liquid, and I use 1 part each day until there are only 5 parts fluid, then replace the sixth part with water, and repeat the cycle, how many days until the solution is 10% or less of the original solution?

 

[MitchSchaft]

5 ..

 

[fury]

12, I think.

 

[unclehobart]

im getting roughly 13 days

 

[unclehobart]

12 days is high 10% ... 13 is under 10%. It just depends upon how strict you are.

 

[Luis G]

agree with unc.

 

[markjs]

Thank you! I wonder where he got 5? No matter...I had guessed 12, but with no basis other than that it felt right....

 

[unclehobart]

.833> .693889> 0.578009537> 0.481481944321> 0.401...> 0.334...> 0.2783...> 0.2318...> 0.1931...> 0.1608...> 0.133996...> 0.1116...> 0.092979...

 

[MitchSchaft]

It was just a guess . Close enough!

 

[fury]

Oh. I was going by 6 * 0.83 multiple times and then counting how many times it took to get under 0.6.

 

[unclehobart]

I did it as 8.333 even though its 8.33333333333333333>. You never know when those little fragments will come back to haunt you.

 

[fury]

I did 0.833~ (as many 3's as calc let me do)

 

[Luis G]

(5/6) ^ 12 = 244,140,625 / 2,176,782,336 =~ 0.112156654
(5/6) ^ 13 = 1,220,703,125 / 13,060,694,016 =~ 0.093453878

There you go your precision

 

[Shadowfax]

Geez...nobody around here uses Maple?

 

[unclehobart]

The math would be a serious bitch if your base liquid was mercury. I dare say 10% would never be achieved.