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1. 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, 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.​

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elcharly64

Answer:

[tex]C(t)=5\cdot(0.9)^t[/tex]

Step-by-step explanation:

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

[tex]C(t)=C_o\cdot(1-r)^t[/tex]

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The concentration of the pollutants starts at Co=5 mg/lt. We also know the pollutant reduces its concentration by 10% each hour. This gives us a value of r = 10% / 100 = 0.1

Substituting into the general equation:

[tex]C(t)=5\cdot(1-0.1)^t[/tex]

Operating:

[tex]\boxed{C(t)=5\cdot(0.9)^t}[/tex]

y(n) = 5(0.9)ⁿ

  • To answer this, we will make use of the exponential decaying function which is given by;

y(n) = a(1 - b)ⁿ

where;

y is the final amount at time n,

a is the original amount

b is the decay factor

x is the amount of time that has passed.

  • We are told that the initial concentration of the pollutants is 5 mg/L

Thus;

a = 5 mg/L.

We are told that the pollutant reduces its concentration by 10% each hour. Thus; b= 10%

b = 0.1

  • Therefore Plugging in the relevant values into y(n) = a(1 - b)ⁿ, we have;

y(n) = 5(1 - 0.1)ⁿ

y(n) = 5(0.9)ⁿ

Read more at; brainly.com/question/2046253

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