i need help exam on wed.

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. Round your answer to one decimal place. 

How much contaminant is removed from the tenth (t = 10)

 to the thirteenth (t = 13)

 hour of the cleaning process? 

Answer 1

You're starting with 100 lbs of contaminant. You remove 20% per hour, so every hour you have 80% left of the starting amount. Do that for 13 hours. Since they want the amount of contaminant removed, you have to subtract the amount left at hour 13 from the amount you had at hour 10. There might be a mathematical formula you can use to do this calculation in one step, but the problem is still doable even if you don't know that mathematical formula.

1: 100*80%= 80 lbs contaminant

2: 80*80%= 64 

3: 64*80%=51.2

4: 51.2*80 = 41.0

5: 41.0*80 = 32.8

6: 32.8*80 =26.2

7: 26.2*80 = 21.0

8: 21.0*80= 16.8

9: 16.8*80 =13.4

10: 13.4*80= 10.7

11: 10.7*80 = 8.59

12: 8.59*80 = 6.87

13: 6.87*80 = 5.50

Therefore, 10.7 - 5.5= 5.2 lbs removed from t=10 to t=13