Question

A tank is full and holds 600 gallons of water. It is being pumped out at a rate of 30 gallons per hour. Let y be the number of gallons in the tank. Is it discrete or continuous? And what are they domain and range?

Answer 1

The volume of water in the tank can be expressed by the equation below:

`y(t)\text{ = 600-30}\cdot t`

Where y is the volume of the tank and t is the time elapsed since the tank started pumping water out.

A function is continuous when it is difined for all the values inside its domain. The domain of this function is all the positive real numbers, this is because the input represents time and there isn't negative time. For each fraction of hour there will be an associated volume of water in the tank, therefore the function is continuous.

The domain of the function is:

`(0,\infty(`

The range of the function is the set of values that it can output for the given domain. In this case the maximum value of the function is the total capacity of the tank 600 gallons, while the minimum value happens when the tank is empty, so the range is:

`(0,600)`