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.Com
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)   (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)   (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.


RELATED QUESTIONS

Joe has a 15 gallon fish tank. The tank currently has 7 quarts of water in it. How many... (answered by Alan3354)
Twenty water tanks are decreasing in size in such a way that the volume of each tank is... (answered by Alan3354)
A water storage tank has a volume of 6,740 cubic feet. When the tank is 3/4 full, how... (answered by josgarithmetic)
A cleaning liquid contains three main ingredients, water, wax and white sprits, mixed in... (answered by Fombitz)
A cleaning liquid contains three main ingredients; water, wax and white spirits. Mixed... (answered by josmiceli)
A tank can hold 122,000 gallons of liquid. If the tank is filled 3/4 of the way how many... (answered by rfer)
how many water to be filled in a tank to 1 inch height, area of tank is 1000 square... (answered by Alan3354)
The proportion of water and liquid soap in a certain cleaning fluid be 5:2. There are 6... (answered by amarjeeth123)
A cylindrical tank has an 18 inch diameter and is 20 inches high. If it is half full of... (answered by lwsshak3)