[填空题]
In a water filtration plant, the containez h2b)r: az0 f/6n7 pp7eklmdars bgbv2 zly; qyuacglr8 d : w:q48v--w5of water are filled and then filtered, all by an automated system. The volume of water in a container, W(t), in litres, after t seconds of the fillinv4cgdlvabu2 8qr gz 8qwwby;5l-y::-g commencing can be modelled by the function
W(t)=V(1−$e^{\frac{-t}{k}}$),where V is the maximum volume of the water container and k is a positive constant used to alter the rate at which water is filling the containers.
The value of k is currently set at 25.
1.Find how long it takes, t, for a container to fill up to 50% of its maximum volume. t ≈ seconds
2.If one of the containers has a maximum volume of 20 litres, find the volume of water in this container after 22 seconds. W ≈ litres
The engineers of the plant want to alter the value of k so that it takes 20 seconds to fill each container up to 95% of their maximum volumes.
3.Find the value of k required. k ≈
