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
Accepted Solution
A:
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 [tex] \frac{1}{55-50} \times \frac{-124}{11} \int\limits^{55}_{50} {(\frac{1}{x+10}+\frac{10}{x-100})} \, dx[/tex] 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