1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C = __6,000__ (all supposed to be underlined)
300-3x
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.
Type divisions this way ...
C = 6000/(300-x)
a) replace x with 75
C = 6000/(300-3(75))
= 6000/75 = 80
b) you try it, should get 200
c) should be really high
d) what happens when x = 100 ?
For A...I have 80million
B...200million
C...58 million
c)
C = 6000/(300 - 3(99))
= 6000/3
= 2000 million
ok i did it like this:
6000/(300-3*99)
oh!!! never mind got it now..thank you!!!!
To answer these questions, we will substitute the given values of x into the equation C = 6,000/(300-3x) and solve for each part.
a. To find the cost to remove 75% of the pollutant, we substitute x = 75 into the equation:
C = 6,000/(300-3*75) = 6,000/(300-225) = 6,000/75 = 80
Therefore, the cost to remove 75% of the pollutant is $80 million.
b. To find the cost to remove 90% of the pollutant, we substitute x = 90 into the equation:
C = 6,000/(300-3*90) = 6,000/(300-270) = 6,000/30 = 200
Therefore, the cost to remove 90% of the pollutant is $200 million.
c. To find the cost to remove 99% of the pollutant, we substitute x = 99 into the equation:
C = 6,000/(300-3*99) = 6,000/(300-297) = 6,000/3 = 2,000
Therefore, the cost to remove 99% of the pollutant is $2,000 million.
d. To find for what value this equation is undefined, we look at the denominator, which is (300-3x). The equation will be undefined when the denominator becomes zero because division by zero is undefined. So, we set the denominator equal to zero and solve for x:
300-3x = 0
-3x = -300
x = 100
Therefore, the equation is undefined for x = 100.
e. The answers to sections a. through c. match expectations because they provide the cost in millions of dollars to remove a certain percentage of the pollutant as specified by the values of x.
However, the answer to section d. might be unexpected because the equation becomes undefined when x = 100. This means that it is not possible to remove 100% or more of the pollutant according to this model.