Question

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 20% of the remaining contaminant each hour. How much contaminant is removed during the first three hours

Answer 1

Answer:

The amount of the contaminant removed during the first three hours will be 48.8 pounds.

Step-by-step explanation:

There, in a large tank of water, are initially 100 pounds of a contaminant.

Also given that the cleaning method removes 20% of the remaining contaminant each hour.

So, after the first hour, the amount of the contaminant will remain by $100(1 - \frac{20}{100}) = 80$ pounds.

Now, after the second hour, the amount of the contaminant will remain by

$80(1 - \frac{20}{100}) = 64$ pounds.

Finally, after the third hour, the amount of the contaminant will remain by $64(1 - \frac{20}{100}) = 51.2$ pounds.

Therefore, the amount of the contaminant removed during the first three hours will be (100 - 51.2) = 48.8 pounds. (Answer)