SOLUTION: Many physical processes are exponential in nature. A typical way of cleaning a tank of contaminated water is to run in clean water at a constant rate, stir, and let the mixture run

Algebra ->  Linear-equations -> SOLUTION: Many physical processes are exponential in nature. A typical way of cleaning a tank of contaminated water is to run in clean water at a constant rate, stir, and let the mixture run      Log On


   

Question 1127611: Many physical processes are exponential in nature. A typical way of cleaning a tank of contaminated water is to run in clean water at a constant rate, stir, and let the mixture run out at the same rate. Suppose there are initially 100 pounds of a contaminant in a large tank of water. Assume that the cleaning method described above removes 30% of the remaining contaminant each hour.
How much contaminant is removed during the first three hours?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Many physical processes are exponential in nature. A typical way of cleaning a tank of contaminated water is to run in clean water at a constant rate, stir, and let the mixture run out at the same rate. Suppose there are initially 100 pounds of a contaminant in a large tank of water. Assume that the cleaning method described above removes 30% of the remaining contaminant each hour.
How much contaminant is removed during the first three hours?
Start:: 100 lbs of contam.
After one hour:: 0.7*100 = 70 lbs of contam remains
After 2nd hour:: 0.7*70 = 49 lbs of contam remains
After 3rd hour:: 0.7*49 = 34.3 lbs of contam remains
----
Answer:: 100 - 0.7^3*100 = 100 - 0.343*100 = 34.3 of contam remains
Answer:: Amount removed after 3 hrs:: 100 - 34.3 = 65.7 lbs
-----
Cheers,
Stan H.
----------

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
The amount of the removed contaminant in the first hours is 0.3*100 = 30 pounds;  0.7*100 = 70 pounds of the contaminant remained.


The amount of the removed contaminant in the second hours is 0.3*70 = 21 pounds;  70-21 = 49 pounds of the contaminant remained.


The amount of the removed contaminant in the third hours is 0.3*49 = 14.7 pounds;  49-14.7 = 34.3 pounds of the contaminant remained.



Now the total removed mass of the contaminant is 100 - 34.3 = 65.7 pounds.    Answer

Solved.