Question

4. If water is being drained from a swimming pool and V liters is the volume of the water at the time t minutes after the draining starts, where � = 250 1600 − 80� + � 2 , how fast is the water flowing out of the water pool 5 minutes after the draining starts?

Answer 1

Water is leaving at 17500m^3 per minute

Explanation:

Given

`V(t)= 250(1600 - 80t + t^2)`

Required

The rate when time is 5 minutes

We have:

`V(t)= 250(1600 - 80t + t^2)`

Open bracket

`V(t)= 400000 - 20000t + 250t^2`

Differentiate

`V'(t) = 0 - 20000 + 2*250t`

`V'(t) = 0 - 20000 + 500t`

`V'(t) = -20000 + 500t`

At 5 minutes, we have:

`V'(5) = -20000 + 500*5`

`V'(5) = -20000 + 2500`

`V'(5) = -17500`

This means that water is leaving at 17500m^3 per minute