Thread: Estimating with Finite Sums

Water Pollution: Oil is leaking out of a tanker damaged at sea. The damage to the tanker is worsening as evidenced by the increased leakage each hour, recorded in the table below,

Time(h): 0 1 2 3 4
Leakage(gal/h): 50 70 97 136 190

Time(h): 5 6 7 8
Leakage(gal/h): 265 369 516 720

(a)Give an upper & lower estimate of the total quantity of oil that has escaped after 5 hours.

(b)Repeat (a) for the quantity of oil that has escaped after 8 hours.

(c)The tanker continues to leak 720 gal/h after the first 8 hours. If the tanker originally contained 25,000 gal of oil, approxiamately how many more hours will elapse in the worst case before all of the oil has leaked? in the best case?

lower estimate for the first 5 hours ...

(50+70+97+136+190) gals

upper estimate for the first 5 hours ...

(70+97+136+190+265) gals

now, you do (b) and (c)

I know how to do (b) because of (a), however, how do you begin (c)?

worst case ...

70+97+136+190+265+369+516+720+720h = 25000

solve or h

you do the best case.