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?
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, without a t, 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.