1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C=6000/(200-2x).
a. What is the cost to remove 75% of the pollutant?
C=6000/(200-2(.75))
C=6000/(200-1.5)
C=6000/198.5
C=30.2
Is this correct?
This is stumping me to:
For what value is this equation undefined?
Thanks in advance.
To find the cost to remove 75% of the pollutant, you correctly substituted x = 0.75 into the equation C = 6000/(200 - 2x):
C = 6000/(200 - 2(0.75))
C = 6000/(200 - 1.5)
C = 6000/198.5
C ≈ 30.2
So, your answer of C ≈ 30.2 is correct.
Now let's determine for what value the equation is undefined. In this case, the equation C = 6000/(200 - 2x) will be undefined if the denominator (200 - 2x) becomes zero, since division by zero is undefined.
Set the denominator equal to zero and solve for x:
200 - 2x = 0
2x = 200
x = 100/2
x = 50
Therefore, the equation C = 6000/(200 - 2x) is undefined when x = 50.