1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C= 3,000/300-3x.
Please note: x is in percent, not decimal form.
a. What is the cost to remove 75% of the pollutant?
b. What is the cost to remove 90% of the pollutant?
c. What is the cost to remove 99% of the pollutant?
d. For what value is this equation undefined?
e. Do the answers to sections a. through d. match your expectations? Explain why or why not.
for d, when is the denominator zero?
I will be happy to critique your thinking on this. I am uncertain what you are stuck on.
a. C = 3000 / (300 - 3x),
C = 3000 / (300 - 3*75),
C = 3000 / (300 - 225),
C = 3000 / 75 = 40M.
b. Same procedure as a.
c. Same procedure as a.
d. The Eq is undefined when the denominator equals 0:
300 - 3x = 0,
3x = 300,
X = 100%.
So the Eq is undefined when X = 100%.
To find the cost to remove a certain percentage of pollution, we can substitute the given percentage into the equation C = 3,000 / (300 - 3x), where x is the percentage in decimal form.
a. To find the cost to remove 75% of the pollutant, we substitute x = 75% = 0.75 into the equation:
C = 3,000 / (300 - 3(0.75))
C = 3,000 / (300 - 2.25)
C = 3,000 / 297.75
C ≈ 10.08 million dollars
b. To find the cost to remove 90% of the pollutant, we substitute x = 90% = 0.90 into the equation:
C = 3,000 / (300 - 3(0.90))
C = 3,000 / (300 - 2.70)
C = 3,000 / 297.30
C ≈ 10.09 million dollars
c. To find the cost to remove 99% of the pollutant, we substitute x = 99% = 0.99 into the equation:
C = 3,000 / (300 - 3(0.99))
C = 3,000 / (300 - 2.97)
C = 3,000 / 297.03
C ≈ 10.10 million dollars
d. This equation is undefined when the denominator is equal to zero, because division by zero is not allowed. In this case, the denominator is 300 - 3x. So to find the value that makes this equation undefined, we set the denominator equal to zero and solve for x:
300 - 3x = 0
3x = 300
x = 100
Therefore, this equation is undefined when x = 100%.
e. The answers to sections a. through d. may or may not match expectations depending on the specific situation and context. It is important to analyze the equation and understand its behavior to determine if the answers align with expectations. In this case, since the equation is rational, we would expect the cost to decrease as the percentage of pollution to be removed increases. The cost increases at a decreasing rate as the percentage approaches 100%. The fact that the equation is undefined at 100% aligns with the expectation that it is not possible to remove 100% of the pollutant.