A tank initially contains 7 gallons of water. A faucet is opened and water begins pouring into the tank at a rate of 1.5 gallons per minute until the tank is full. Which of the following represents the volume V of water in gallons in the tank as a function of time t in minutes that has elapsed since the faucet is opened?

A) v(t)=1.5+t
B)v(t)=8.5+t
C)v(t)=1.5t
D)v(t)=1.5t-7
E)v(t)=1.5t+7
Thanks

The correct answer needs to have 1.5t, because 1.5 gallons go into the tank every minute, and there are t minutes that the faucet is running. It also needs to have a +7, withoutt, because that original 7 gallons in the tank is the starting point—it doesn’t change with the amount of time the faucet has been running.

A good mental roadmap for a question like this is to start by noting how much was in the tank before the faucet was turned on, which is time 0. The question tells us that at time 0, there were 7 gallons in the tank, so we should be able to plug 0 in for t in the right answer and get 7. Only choice E does that, so we’re done. If that didn’t eliminate every choice, though, then the next step would be to figure out that after 1 minute of the faucet running, there should be 8.5 gallons in the tank. Of the choices not yet eliminated, which gives you 8.5 when t = 1? Etc. Omniaa Ali says:

I agree with you but why not c ? The question says that has elapsed since the faucet was opened so without the 7 gallons that were initially there ? What do you think ? Thanks a lot Mike McClenathan says:

No. The volume if water in the tank includes the 7 originally there. Omniaa Ali says:

I know but it says it wants the volume of water since the faucet was opened so ignoring the 7gallons already there ? Mike McClenathan says:

I assure, you, with 100% certainty, that as this question is worded the correct answer is E. It says, “the volume V of water in gallons in the tank as a function of time t in minutes that has elapsed since the faucet is opened.” Look at that in 2 parts. The first part is, “the volume V of water in gallons in the tank.” The second part is, “as a function of time t in minutes that has elapsed since the faucet is opened.” Obviously, the amount of water begins to change once the faucet is opened, so the TOTAL VOLUME can be calculated as a function of time. Omniaa Ali says:

So they want all the volume not the volume for the water sinnce faucet opened till full which is 1.5t right? If yes how will thquestion be like if i wanted to say 1.5t? Mike McClenathan says:

If the answer was 1.5t, then the question would say something like “what is the volume of water that has been added since the faucet was turned on?”