Draining a tank Water is drained from a 3000-gal lank at a rate that starts at 100 gal/hr and decreases continuously by 5%/hr. If the drain is left open indefinitely, how much water is drained from the tank? Can a full tank be emptied at this rate?

Solution:-

Step1

Given that

Water is drained from a 3000-gal lank at a rate that starts at 100 gal/hr and decreases continuously by 5%/hr. If the drain is left open indefinitely.

Step2

To find

how much water is drained from the tank? Can a full tank be emptied at this rate?

Step3

Volume of tank = 3000 gal

Let that the initial rate of draining is 100 gal per hour and then it decreases continuously by 5%/hr

R(t)=100

=

Integrate both side we get,

dt

=dt

=100

=gal

So, Volume of tank = 3000 gal and 2000gal water is drained from the tank.

Therefore,A full tank can not be emptied at this rate.