Sketch and label

Question

Sketch a graph to represent the situation.label each section.

 

The depth of the water in feet in a bathtub increased as gallons of water were added.someone getsin, stays in for a period of time, then gets out and empties and bathtub.

Answer 1

The idea here is to think about how much water is in the tub at a specific time. And of course different times have different things happening. The best way to organize this is to make a table of values. Make a T-chart, and label the first column Time and the second column Depth.

Now, let's say at the moment right before you begin filling up the tub you decide to enter the numbers for Time and Depth. Well, you haven't started the timer yet and there's no water, so put in 0 for both Time and Depth.

After 1 minute maybe the depth is say 2 inches so put in those numbers in your chart. After 2 minutes the depth is 4 inches. After 3 minutes, it is 6 inches. And after 4 minutes it is 8 inches. That's probably when the person would get in, and presumably turn off the water.

Let's assume the person gets in after one minute because the water is too hot. So at 5 minutes when they get in the water depth is now what?

If you've paid attention you know the water rises because the person's body displaces the water and forces it up, thus making the water depth increase. You could experiment with a ruler or tape measure but for the sake of simplicity let's just say it rises to 13 inches. So put 5 and 13 in your chart for time and depth, respectively.

It is important to line up each row of numbers so they are are in fact on the same line and not crooked.

What's happening at 6 minutes after this started? Or 7 minutes? The person is simply sitting there, presumably not moving much, just relaxing. So the depth is not changing from that last measurement of 13 inches.

The only question is how long is the person sitting there? How long do you sit in a warm bath? Maybe 10 minutes? OK, then, starting at 6 minutes in your chart put 13, then 7 minutes put 13 again. So far that's how many minutes in the tub? The person got in at the 5-minute mark so at the 7-minute mark 2 minutes have passed. So 8 in your chart would correspond to 3 minutes in the tub (and the height still being 13 inches), 9 would correspond to 4 minutes in the tub, and so on. When do you stop?

Just count. Keep counting: 9 is 4, 10 is 5, 11 is 6, and up until you reach a ten-minute bath. That would be at the 15-minute mark. And what's the depth from the 5-minute mark until the 15-minute mark? 13 inches for every minute because no water was added and the person was still.

Your chart or table of values should have a lot of numbers in it from 0 to 15 in the Time column and from 0 to 13 in the Depth column.

When they get out, the water level returns to the same level at the 4 minute mark. The water begins to drain so the depth numbers start to drop for every minute that passes. This is an interesting phenomenon that would be happening: the pressure of the water when it is full causes the water to drain faster than when it is less full, so the numbers may drop from the 8-inch depth faster for the first couple of minutes, but then slow down for the last few minutes as it becomes more empty.

Lastly, you simply plot these points on a graph, making sure to plot the time and corresponding depth figures carefully. It's a good idea to look at your graph and see if it makes sense. Can the depth be at two different points on your graph at the same minute? Hmm, no that doesn't make sense. So you might need to adjust your graph to make it fit reality!