The function f(x)=(250x)/(100-x) models the cost, f(x), in millions of dollars, to remove x% of a river's pollutants. Use this functions to solve: If the government commits $750 million for this project, what percentage of the pollutants can be removed?
To solve this problem, we need to find the value of x, which represents the percentage of pollutants that can be removed when the cost is $750 million.
Given the function f(x) = (250x) / (100 - x), we can set up the equation as follows:
(250x) / (100 - x) = 750
To solve for x, we need to isolate it on one side of the equation. Let's start by multiplying both sides of the equation by (100 - x) to eliminate the denominator:
250x = 750(100 - x)
Now, let's distribute the 750 on the right side of the equation:
250x = 75000 - 750x
Next, let's combine like terms by adding 750x to both sides of the equation:
250x + 750x = 75000
Combine the x terms:
1000x = 75000
To solve for x, divide both sides of the equation by 1000:
x = 75000 / 1000
Simplifying, we get:
x = 75
Therefore, 75% of the pollutants can be removed when the government commits $750 million for the project.