The cost, in millions of dollars, to remove x% of pollution in a lake modeled by C=6,000/200-2x
What is the cost to remove 75% of the pollutant?
90%
99%
For what value is theis equation undefined?
Just plug in numbers and calculate. In the case of 75% the asnwer is
C = 6,000/(200-150) = $120 (Million$)
The equation is defined for o<=x<100 (%)
To find the cost of removing a certain percentage of pollution, we can substitute the given percentage into the equation for C.
Let's start by finding the cost to remove 75% of the pollutant. We can substitute x = 75 in the formula C = 6,000 / (200 - 2x).
C = 6,000 / (200 - 2(75))
C = 6,000 / (200 - 150)
C = 6,000 / 50
C = 120
Therefore, the cost to remove 75% of the pollutant is $120 million.
Now let's find the cost to remove 90% of the pollutant by substituting x = 90.
C = 6,000 / (200 - 2(90))
C = 6,000 / (200 - 180)
C = 6,000 / 20
C = 300
Therefore, the cost to remove 90% of the pollutant is $300 million.
Next, let's find the cost to remove 99% of the pollutant by substituting x = 99.
C = 6,000 / (200 - 2(99))
C = 6,000 / (200 - 198)
C = 6,000 / 2
C = 3,000
Therefore, the cost to remove 99% of the pollutant is $3,000 million.
Now, let's determine for which value of x the equation is undefined. The equation C = 6,000 / (200 - 2x) will be undefined when the denominator, (200 - 2x), equals zero.
So, let's solve the equation: 200 - 2x = 0.
2x = 200
x = 100
The equation is undefined for x = 100.
In summary:
- The cost to remove 75% of the pollutant is $120 million.
- The cost to remove 90% of the pollutant is $300 million.
- The cost to remove 99% of the pollutant is $3,000 million.
- The equation is undefined for x = 100.