Answer:
a) ![V(t) = 24 - 2t](https://tex.z-dn.net/?f=V%28t%29%20%3D%2024%20-%202t)
b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.
Step-by-step explanation:
The volume of the tank in terms of the time can be described by the following equation:
![V(t) = V(0) - at](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%20-%20at)
In which V(0) is the initial volume and a is the hourly decrease rate.
a. Write a formula that expresses v in terms of t.
The tank initially contains 24 gallons of water, which means that ![V(0) = 24](https://tex.z-dn.net/?f=V%280%29%20%3D%2024)
Drains at a constant rate of 2 gallons per hour, so ![a = 2](https://tex.z-dn.net/?f=a%20%3D%202)
Then
![V(t) = V(0) - at](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%20-%20at)
![V(t) = 24 - 2t](https://tex.z-dn.net/?f=V%28t%29%20%3D%2024%20-%202t)
b. As t increases from 3 to 6, v varies from _________ to _________
![V(t) = 24 - 2t](https://tex.z-dn.net/?f=V%28t%29%20%3D%2024%20-%202t)
![V(3) = 24 - 2*3 = 18](https://tex.z-dn.net/?f=V%283%29%20%3D%2024%20-%202%2A3%20%3D%2018)
![V(6) = 24 - 2*6 = 12](https://tex.z-dn.net/?f=V%286%29%20%3D%2024%20-%202%2A6%20%3D%2012)
So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.