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?

To find the amount of budget needed to remove 90% of the pollutants, you need to substitute x = 90 into the cost function C(x) and then solve for C(90).

Plug x = 90 into the cost function:
C(x) = 25x / (100 - x)
C(90) = 25 * 90 / (100 - 90)
C(90) = 2250 / 10
C(90) = 225

So, the budget should be $225 million.

Now, let's interpret the domain within the context of the text:

a. The domain of the cost function is (-∞, 100). This means that the function is defined for all values of x that are less than 100. In the context of the problem, it implies that the cost function can be used to estimate the cost of removing any percentage of pollutants up to 100%. It is important to note that the cost function is not defined for x = 100 since division by 0 is undefined. So, the cost function cannot be used to estimate the cost of removing 100% of the pollutants.