The cost, in millions of dollars to remove x% of pollution modeled by c=6000/200-2x. 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 eqaution undefined?
just replace x by the percentage value
e.g. for 75% removal
cost = 6000/(200-2(75))
= 120
do the same for the others
as to D) when is the denominator zero?
when 200-2x = 0
for when x = 100
so mathematically you could never pay enough to remove 100% of the pollutants.
BTW, I don't see why the function was not reduced to c = 3000/(100-x) ?
Did the text state it this way?
To find the cost to remove a certain percentage of pollutants, we need to substitute the given percentage into the equation c = 6000 / (200 - 2x).
A) To find the cost of removing 75% of the pollutant, substitute x = 75 into the equation:
c = 6000 / (200 - 2 * 75)
Simplify:
c = 6000 / (200 - 150)
c = 6000 / 50
c = 120
Therefore, the cost to remove 75% of the pollutant is $120 million.
B) To find the cost of removing 90% of the pollutant, substitute x = 90 into the equation:
c = 6000 / (200 - 2 * 90)
Simplify:
c = 6000 / (200 - 180)
c = 6000 / 20
c = 300
Therefore, the cost to remove 90% of the pollutant is $300 million.
C) To find the cost of removing 99% of the pollutant, substitute x = 99 into the equation:
c = 6000 / (200 - 2 * 99)
Simplify:
c = 6000 / (200 - 198)
c = 6000 / 2
c = 3000
Therefore, the cost to remove 99% of the pollutant is $3000 million (or $3 billion).
D) The equation c = 6000 / (200 - 2x) is undefined when the denominator (200 - 2x) equals zero. To find the value for which the equation is undefined, set the denominator equal to zero and solve for x:
200 - 2x = 0
2x = 200
x = 100
Therefore, the equation is undefined for x = 100.