Reef Chemistry Question of the Day #103 Water Change Efficiency

[Randy Holmes-Farley]

Reef Chemistry Question of the Day #103

One water change that replaces 30% of the aquarium's water obviously removes 30% of a pollutant in that water (assuming that none is in the new water and no special reservoir such as bound to rock or sand) and leaves 70% behind. If, instead, a series of 30 water changes, each replacing 1% of the total water, are performed, how much of the original pollutant will remain?


A. 99%
B. 90%
C. 74%
D. 50%

 

[tonizzy22]

Answer is C the more frequent smaller amount water change is less effective because each time you do a water change you are now diluting the original pollutants and cant remove the same amount with each wc.

 

[omykiss001]

C is what I get using an exponential decay function.

 

[beaslbob]

when you don't know again it's C.

 

[beaslbob]

Pssst:
using excel Power(.99,30)=

0.73970037338828000000

 

[beaslbob]

Now on a more intuitive method.
It cannot be less than the one time water change. So d is out.
with 30 changes it should be relatively close but above the one time change. to 99 % and 90% are out (99% is just one change anyway)
So the only thing that makes any sense is 74% even if you don't have a calculator or excel or (back in my day) lost your slide rule.

 

[Steven@]

fun brain teaser... C

 

[tonizzy22]

Pssst:
using excel Power(.99,30)=

0.73970037338828000000

What formula do you use in excel to figure this out?

 

[beaslbob]

What formula do you use in excel to figure this out?

The excell power function. power(.99,30) is excel's function (.99)^30 Power(.99;30)

Woopsies the comma should have been a semicolon.

 

[Randy Holmes-Farley]

And the answer is (as everyone here knew)...C. 74%

I used my calculator. 0.99³⁰