Question

Suppose a cost-benefit model is given by y = 4.6x-:100-x , where y is the cost in thousands of dollars for removing x percent of a given pollutant. find the cost of removing 35%

Answer 1

Final Answer;

The cost of removing 35% of the given pollutant is $1,725.

Explanation;

The given cost-benefit model is represented by the equation
`(y = 4.6x - frac{100}{x})`, where (y) is the cost in thousands of dollars for removing (x) percent of the pollutant. To find the cost of removing 35% substitute
`(x = 35%)`into the equation:

`[y = 4.6 times 35 - frac{100}{35]`

Simplifying further:

`[y = 161 - 2.857]`

Thus, (y = 158.143) represents the cost in thousands of dollars. To convert this to actual dollars, we multiply by 1000:

[158.143 times 1000 = $158 143]

Therefore the cost of removing 35% of the pollutant is $158 143.

In the context of environmental management or industry compliance, understanding such cost-benefit models is crucial. The equation encapsulates both a linear relationship (4.6x) and an inversely proportional relationship
`(\((100)/(x)\))` reflecting the balance between the efficiency and cost of pollutant removal. In this case, the cost is influenced by both the percentage to be removed and the fixed cost term. The resul
`t $158143` provides a tangible figure that decision-makers can utilize in budgeting and strategizing pollution control measures emphasizing the economic aspects of environmental stewardship.