Question

The graph shows the height of the water in a bathtub as a function of time. Give a verbal description of what you think happened.

Short answer

The verbal description of the graph is shown below.

Step-by-step solution

Given information

Consider the given graph.

Describe the given graph condition

From the graph, it can be observed that in the first five minutes there is a linear increase in the height of the water and the height in \(15\) inches. This means that the tub was being filled in the first 5 minutes.

It can also be observed that there is a sudden increase in height (about 5 inches). This means that the person that filled the bathtub entered it and started bathing.

From the graph, it can be observed that the height is constant for the next 7-8 minutes, which can be interpreted as the person being in the bathtub.

Next, there is a slight decrease in height followed by an increase in height which returns the height to the previous level. This means that,

• Some of the water may have spilled during the bath, so the person bathing refilled the tab.
• The water may have cooled off a little so the person bathing drained some of the water and refilled the tub with hot water.
• The person bathing may have partially climbed out of the tub to grab a bar of soap or a bottle of shampoo

Then for the next \(4 - 5\) minutes, the water height is constant, which indicates that the person bathing was finishing the bath. After that, there is a sudden decrease in the height of the water which implies that the person left the tub. After that, there is a linear decrease in water height for the next 3-4 minutes where at the end the height reaches\(0\). This means that the tub was being drained.