contaminated water is subjected to a cleaning process the concentration of the pollutants is initially 5 mg per liter of waters if the cleaning process can reduce the pollutant by 10% each hour 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
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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