Coal gas is produced at a gasworks. Pollutants in the gas are removed by scrubbe

Question

Coal gas is produced at a gasworks. Pollutants in the gas are removed by scrubbers, which become less and less efficient as time goes on. The following measurements, made at the start of each month, show the rate at which pollutants are escaping (in tons/month) in the gas: Make an overestimate and an underestimate of the total quantity of pollutants that escape during the first month. Make an overestimate and an underestimate of the total quantity of pollutants that escape for the whole six months for which we have data. How often would measurements have to be made to find an overestimate and an underestimate (for the quantity of pollutants that escaped) during the first six months which differ by exactly 1 ton from each other?

Explanation / Answer

Answers for Part A and Part B are correct.

Solution for Part C is as follows :

If measurements are made every "t" months, and the rate is given by f(t), then the difference (error in estimate) is |f(6)-f(0)| * t. For this to be 1 ton, we have the equation :

|f(6)-f(0)| * t = 1

(45-7)*t = 1

38*t = 1

t = 1/38

So, the answer is : 38 times a month.

I see you have entered 39 as the answer in the software. Please change 39 to 38.

Please try entering 38 into the software, and the answer would be correct.

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