Estimating with Finite Sums

• Jan 19th 2009, 05:20 PM
katchat64
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?
• Jan 19th 2009, 05:50 PM
skeeter
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)
• Jan 19th 2009, 06:40 PM
katchat64
How to start on (c)
I know how to do (b) because of (a), however, how do you begin (c)?
• Jan 20th 2009, 01:36 PM
skeeter
worst case ...

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

solve or h

you do the best case.