A swimming pool is to be drained by cleaning. If L represents the number of litres of water in the pool `t` seconds after the pool has been plugged off to drain and `L=2000(10-t)^2dot` How fast is the water ruining out at the end of 5 seconds? What is the average rate at which the water flows out during the first 5 seconds?

Explanation

Let L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain, then
`L=200(10-t)^(2)`
`therefore` Rate at which the water is running out `=-(dL)/(dt)`
`(dL)/(dt) = -200.2(10-t).(-1)`
`=400(10-t)`
Rate at which the water is running out at the end of 5s
`=400(10-5)`
`=2000L//s `= Final rate
Since, initial rate `=-(dL)/(dt)_(t=0) = 4000 L//s`
`therefore` Average rate during 5s `=("Initial rate + Final rate")/(2)`
`=(4000+2000)/(2)`
`=3000L//s`