Question

Dana is filling a 1.5 gallon watering can at a rate of 0.75 gallon per minute. What is the domain of the function that represents the volume of water in the can after x minutes?

Answer 1

The domain of the function is
`Dom \{y\} = [0\,min, 2\,min]`.

Explanation:

We understand that the watering can is filled at a constant rate, that is:

`y =k\cdot x`

Where:

`x` - Filling time, measured in minutes.

`y` - Watering can volume occupied by water, measured in gallons.

`k` - Filling rate, measured in gallons per minute.

If we know that
`k = 0.75\,(gal)/(min)` and
`y = 1.5\,gal`, the final filling time is:

`x = (y)/(k)`

`x = (1.5\,gal)/(0.75\,(gal)/(min) )`

`x = 2\,min`

The domain of the function corresponds to the set of real numbers between zero and final filling time. That is to say:

`Dom \{y\} = [0\,min, 2\,min]`