Question

(1 point) 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 8 12 16 23 32 44 A. Make an overestimate and an underestimate of the total quantity of pollutants that escape during the first month. overestimate = tons underestimate = 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 = underestimate = 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? times a month.

Answer 1

Part A

Overestimate = Riemann right sum

Underestimate = Riemann left sum

Overestimate = 8 tons

Underestimate = 7 tons

Part B

Overestimate = 135 tons (8+12+16+23+32+44)

Underestimate = 98 tons (7+8+12+16+23+32)

Part C

37 times a month

|f(6)-f(0)|*Δt = 1

(44-7) *Δt = 1

37*Δt = 1

Δt = 1/37

37 times a month to get a difference between the over- and underestimates of only 1 ton