The functionf(x) = 300x/100-x models the cost, F(x) in m illions of dollars to remove x% of a rivers pollutants. If the government commits $325 million for this project, what percentage of the pollutants can be removed?
I will assume you meant
f(x) = 300x/(100-x)
so if f(x) = 325
325 = 300x/(100-x)
32500 - 325x = 300x
32500 = 625x
x = 32500/625 = 52
so 52% has been removed.
F(x) = 300X/(100-X) = $325M.
300X/(100-X) = 325,
Multiply both sides by 100-X:
30000X - 300X^2 = 32500 - 325X,
-300X^2 + 30000X + 325X-32,500 = 0,
-300X^2 + 30,325X - 32,500 = 0,
Divide both sides by -25:
12X^2 - 1213 + 1300 = 0,
Solve using the Quadratic Formula and
get:
X = 1.083%, and x = 100%.
Solution: X = 1.08333%.
OOPS! CORRECTION.
Multiply both sides by 100-X and get:
300X = (100-X)325,
300X = 32500 - 325X,
300X + 325X = 32500,
625X = 32500,
X = 52%.
To find the percentage of pollutants that can be removed, we need to consider the cost function and the amount of money allocated for the project.
Given:
The cost function is f(x) = 300x / (100 - x), where f(x) represents the cost in millions of dollars to remove x% of the pollutants.
The government has allocated $325 million for the project.
To find the percentage of pollutants that can be removed, we need to find the value of x for which the cost function equals $325 million.
Step 1: Set up the equation
The cost function f(x) is given as f(x) = 300x / (100 - x).
We want to find the value of x for which f(x) equals $325 million.
So, we have the equation: 300x / (100 - x) = 325.
Step 2: Solve the equation
To solve the equation, we can start by multiplying both sides by (100 - x) to eliminate the denominator:
300x = 325(100 - x).
Expanding the right side:
300x = 32500 - 325x.
Combining like terms:
300x + 325x = 32500.
Simplifying:
625x = 32500.
Dividing both sides by 625:
x = 32500 / 625.
Calculating the value of x:
x = 52.
Step 3: Interpret the result
The value of x is 52, which indicates that 52% of the pollutants can be removed.
Therefore, to remove 52% of the pollutants, the government needs to allocate $325 million for this project.