Question

The predicted cost c (in hundreds of thousands of dollars) for a company to remove p% of a chemical from its waste water is shown in the table. a model for the data is given below. use the model to find the average cost for removing between 50% and 55% of the chemical. (round your answer to two decimal places.) c = 124p (10 + p)(100 – p) , 0 ≤ p < 100 average cost ≈ hundred thousand dollars

Answer 1

We presume your cost function is
c(p) = 124p/((10 +p)(100 -p))

This can be rewritten as
c(p) = (124/11)*(10/(100 -p) -1/(10 +p))

The average value of this function over the interval [50, 55] is given by the integral

`(1)/(55-50) * (-124)/(11) \int\limits^(55)_(50) {((1)/(x+10)+(10)/(x-100))} \, dx`
This evaluates to
(-124/55)*(ln(65/60)+10ln(45/50)) ≈ 2.19494

The average cost of removal of 50-55% of pollutants is about
$2.19 hundred thousand = $219,000