Water flows from the bottom of a storage tank at a rate of r(t) = 400 − 8t liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 45 minutes.

Answer 1

From a gentle stand point...
There are only 400 L in the tank.
r(t) = 400 − 8t
If time is 45 minutes then
r(t) = 400 - 8(45)
= 400 - 360
= 40
So 360 Litres has left the tank : )

Answer 2

r(t) = 400 − 8t
If v is the volume, r(t) = dv/dt. So,
v(t) = 400t - 4t^2
v(45) = 9900