Question

An empty bathtub is filled at a constant rate of 8 gallons per minute. The bathtub will hold 36

gallons of water when full. The volume. V. of water in the bathtub is a function of t. the time
in minutes.
Which is the best description for the domain of the function V?

Answer 1

0 ≤ t ≤ 4.5.

Explanation:

Since the volume of the tub, V is increasing at a rate of 8 gallons per minute, the volume of the bathtub at any time, t is V = 8t.

Now, to find the domain of the function, V, we know that the minimum value for V is zero and the maximum value is 36. Now, at V = 0,

V = 8t

0 = 8t

t = 0 and at V = 36 gallons,

V = 8t

36 = 8t

t = 36/8

t = 4.5 minutes

Since 0 ≤ V ≤ 36, 0 ≤ t ≤ 4.5.

So, the domain of the function V is 0 ≤ t ≤ 4.5.