Question

Water flows from the bottom of a storage tank at a rate of r(t) = 200 − 4t liters per minute, where 0 ≤ t ≤ 50. find the amount of water that flows from the tank during the first 35 minutes.

Answer 1

The answer for your problem is shown on the picture.

Answer 2

Answer:

The amount of water that flows from the tank during the first 35 minutes is 4550 liters.

Step-by-step explanation:

We know that the rate is given by $r(t)=200-4t$ and the problem asks for the net change (the amount of water) for the first 35 minutes.

We can use the Net change theorem:

The integral of a rate of change is the net change:

$\int\limits^b_a {F'(x)} \, dx =F(b)-F(a)$

Applying the above theorem we get

$\int\limits^{35}_0 {200-4t} \, dt$

$\int _0^{35}200dt-\int _0^{35}4tdt\\\\\left[200t\right]^{35}_0-\left[\frac{t^2}{2}\right]^{35}_0\\\\7000-2450\\\\4550$

The amount of water that flows from the tank during the first 35 minutes is 4550 liters.