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:

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:

Time (months) 0 1 2 3 4 5 6
Rate 7 11 18 28 39 50 64
A. Make an overestimate and an underestimate of the total quantity of pollutants that escape during the first month.
overestimate = 11 tons
underestimate = 7 tons

B. Make an overestimate and an underestimate of the total quantity of pollutants that escape for the whole six months for which we have data.
overestimate = 210
underestimate = 153
C. 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?

Answer 1

To find the frequency of measurements needed to get an overestimate and underestimate that differ by exactly 1 ton, we need to find the smallest difference between two adjacent terms in the rate column. From the data, we can see that the smallest difference between two adjacent terms is 4 (between 7 and 11, or between 50 and 64). Therefore, we need to measure the rate at least every 1/4 month (or every week) to achieve the desired level of precision.