The cost in millions to remove x% of pollution in a lake modeled by
C=6000/200-2x.
What is the cost to remove 75% of the pollutant?
What is the cost to remove 99% of the pollutant?
For what value is this equation undefined?
To find the cost to remove a certain percentage of pollution, we can substitute the given percentage into the equation C = 6000 / (200 - 2x).
1. Cost to remove 75% of the pollutant:
We substitute x = 75% = 0.75 into the equation:
C = 6000 / (200 - 2(0.75))
C = 6000 / (200 - 1.5)
C = 6000 / 198.5
C ≈ 30.23 million
Therefore, the cost to remove 75% of the pollutant is approximately 30.23 million.
2. Cost to remove 99% of the pollutant:
We substitute x = 99% = 0.99 into the equation:
C = 6000 / (200 - 2(0.99))
C = 6000 / (200 - 1.98)
C = 6000 / 198.02
C ≈ 30.27 million
Therefore, the cost to remove 99% of the pollutant is approximately 30.27 million.
3. For what value is this equation undefined?
The equation C = 6000 / (200 - 2x) is undefined when the denominator (200 - 2x) equals zero. Therefore, we need to solve the equation 200 - 2x = 0.
200 - 2x = 0
2x = 200
x = 200 / 2
x = 100
Hence, the equation is undefined for x = 100.