Estimate the value of the quantity.

Question

Estimate the value of the quantity.

A swimming pool has a leak. The leak is getting worse. The following table gives the leak rate every 6 hours.

TIME (HR) LEAKAGE (GAL/HR)

0 0

6 .5

12 .7

18 1.1

24 2.4

30 4.5

36 5.6

42 6

48 6.9

Suppose it keeps leaking 6.9 gallons every 6 hours. After losing 2500 gallons the leak is fixed. Approximately how long did the leak last? Use the right endpoints to estimate the first 48 hours.

MULTIPLE CHOICE

33.54 hours

27.54 hours

-93.20 hours

53.64 hours

Answer 1

V = int(dV/dt)dt) you are given the rate at different times. I believe you are supposed to use the right side rectangle approximation:

After 48 hours, the V = (6.9 gal/6 hours)(t-48) or use t after 48

V = 6hr( 6.5 + 12.7 + .... + 486.9 gal/hr)

since the last interval is 6 x 486.9 we're already over 2500. so the limit has to happen in the first 48 hours

I would just do 6 hrs * 6.5 gal/hr + 6*12.7 + ... until I hit > 2500 gal

I'd estimate the time as the midpoint in the t interval to the left of the last side I used. You could also linearly interpolate to the last value, but it's unnecessary with the MC format. Basically, add up to 30 hrs. If you hit, answer is 27 and, 33.5 otherwise.