Question

Environmental Cost The cost C (in millions of dollars) of removing x percent of the pollutants emitted from the smokestack of a factory can be modeled by C = 7x 100 - x (a) What is the implied domain of C? (Enter your answer using interval notation.) Explain your reasoning. Since we are removing pollutants, only negative x-values make sense in this context. Negative x-values and values greater than 100 do not make sense in this context. Also, C(100) is undefined. The function is defined for all x-values except x = 100. It would be cost prohibitive to remove more than 80% of the pollutants. You cannot remove 0% of the pollutants. (b) Use a graphing utility to graph the cost function. Is the function continuous on its domain? Explain your reasoning. OC is continuous on its domain because C is a polynomial. OC is not continuous on its domain because C has a removable discontinuity at x = 7. OC is not continuous on its domain because C has a nonremovable discontinuity at x = -7. OC is not continuous on its domain because C is not a polynomial. C is continuous on its domain because all rational functions are continuous on their domains. (c) Find the cost of removing 65% of the pollutants from the smokestack. $ million

Answer 1

(2) Negative we have 4x ((x)= 150-k (a) implied domain is, (0, 100) x-value and greater them 100 do not make sense in this contest. Also, e(100) is undefined (6) c is continuous on its domain because all rational function are continues on their domeins. put x = 65 e (65) 7 (65) 100-65 13 million dollars