Question

Environmental scientists often use cost-benefit models to estimate the cost of removing a pollutant from the environment as a function of the percentage of pollutant removed. Suppose a cost benefit function for the cost C (in millions of dollars) of removing x percent of the pollutants from Maple Lake is given by

C(x) = 25x/100-x
a. Find the domain and interpret what it means within the text.
The domain is(-óó,100)

b. If federal government wants to remove 90% of the pollutants, how much should the budget be?

Answer 1

clearly the domain is not (-oo,100)
negative percent makes no sense. I'd say the domain is [0,100)

C(X) -> oo as x->100, meaning that the harder you try to squeeze out that last bit of pollution, the morse it costs.

So, just evaluate C(90).
Then double that, since we're talking about a government effort...