Contaminated water is subjected to a cleaning process. The concentration of the pollutants is initially 5 mg per liter of water. if the cleaning process can reduce the pollutant by 10% each our; define a function that can represent the concentration of pollutants in the water in terms of the number of hours that the cleaning process has taken place?
Answers
Answer:
0.9^n x 5
Step-by-step explanation:
As per given information, we can derive and write the function as
Initial concentration of untreated or polluted water water = 5 mg per litre
Pollutants reduce by 10% every hour
Pollutants remaining after an hour would be = (100-10)/100 x 5
Pollutants remaining after an hour would be = (0.9) x 5 = 4.5
Pollutants remaining after two hours would be = 0.9 x (0.9) x 5
Pollutants remaining after nth hour of treatment would be = 0.9^n x 5
Given : Contaminated water is subjected to a cleaning process. The concentration of the pollutants is initially 5 mg per liter of water. if the cleaning process can reduce the pollutant by 10% each hour;
To Find : define a function that can represent the concentration of pollutants in the water in terms of the number of hours that the cleaning process has taken place?
Solution:
Pollutant 5 mg per litre
After one hour = 5 ( 1 - 10/100) = 0.9 * 5
After 2 hours = 0.9 * 5 * (1 - 10/100) = 0.9² * 5
After 3 hours = 0.9² * 5 * (1 - 10/100) = 0.9³ * 5
After n hours = 0.9ⁿ * 5
f(n) = 0.9ⁿ * 5 mg/litre
n = number of hours that the cleaning process has taken place
f(n) = Concentration of pollutants
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