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Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by C(p) = 6800p 100 − p
a. Is C(p) undefined at any p-value? If so, what value? (If an answer does not exist, enter DNE.)
b. What is the domain of C(p) as given by the equation? (Enter your answer using interval notation.)
c. What is the domain of C(p) in the context of the application? (Enter your answer using interval notation.)

Answer :

Answer:

a) p =100

b) [tex] D = (-\infty, 100) \cup (100, \infty)[/tex]

c) But the real practical domain would be:

[tex] D= [0,100)[/tex]

Since the percent of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100

Step-by-step explanation:

For this case we have the following function:

[tex] C(p) = \frac{6800p}{100-p}[/tex]

Part a

For this case the function is not defined at p =100 since:

[tex] C(100) = \frac{6800*100}{100-100} =DNE[/tex]

Is not defined since we can't divide by 0.

So then the answer would be p =100

Part b

For this case since the function is not defined at p =100 the domain would be given by:

[tex] D = (-\infty, 100) \cup (100, \infty)[/tex]

Part c

But the real practical domain would be:

[tex] D= [0,100)[/tex]

Since the percent of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100

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