Given: L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain and L = 200 (10 – t)²

To find: the rate at which the water is running out of the pool at the end of 5s. And also to find the average rate at which the water flows out during the first 5s.

Explanation: Let the rate at which the water us running out be given by

Given L = 200(10-t)²

Now differentiating the above equation with respect to t, we get

Taking out the constant term, we get

Applying the power rule of differentiation, we get

Now we need to find how fast is the water running out at the end of 5 sec, so finding the value of equation (i) at t = 5, we get the answer.

Hence the rate at which the water is running out of the pool at the end of 5s is 2000 L/s

Now to find the initial rate we will substitute t = 0 in equation (i), we get

……(iii)

So equation (ii) is the final rate and equation (iii) is the initial rate.

Hence the average rate during 5s is

Substituting the corresponding values, we ge

Hence the average rate at which the water flows out during the first 5s is 3000L/s.