Calculate Container Water Volume: Interpreting Time-Function Graph at 14 Minutes

Graph Reading with Time-Function Relationships

Given a graph describing the amount of water in the container as a function of time from the time the water is turned on, how much water will be in the container after 14 minutes of pumping the water?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given a graph describing the amount of water in the container as a function of time from the time the water is turned on, how much water will be in the container after 14 minutes of pumping the water?

Weather222444666888101010121212141414161616181818202020222222242424262626282828303030Amount of water202020404040606060808080100100100120120120140140140160160160180180180200200200220220220240240240260260260280280280300300300000CCC111

2

Step-by-step solution

To solve this problem, we need to read and interpret the provided graph that represents the amount of water in a container as a function of time. Let's follow these steps:

  • Step 1: Locate the x-coordinate time value of 14 on the x-axis, which represents the time in minutes.
  • Step 2: Find the corresponding point on the graph directly above this x-coordinate.
  • Step 3: Read the y-coordinate from the graph at this point, which represents the amount of water in the container.

From the graph, at 14 minutes, the point on the graph lines up with the y-coordinate of 160. This means, at 14 minutes, there are 160 units of water in the container. We are assuming a constant graph scaling and spacing for accurate reading.

Therefore, the solution to the problem is 160 160 .

3

Final Answer

160

Key Points to Remember

Essential concepts to master this topic
  • Graph Reading: Find x-value, trace up to curve, read y-value
  • Technique: At x = 14 minutes, trace vertically to graph line
  • Check: Verify point lies on curve and y-axis shows 160 ✓

Common Mistakes

Avoid these frequent errors
  • Reading the wrong axis values
    Don't read the x-axis value when looking for water amount = gives time instead of volume! This confuses the input (time) with output (water amount). Always read the y-axis value at your desired x-coordinate.

Practice Quiz

Test your knowledge with interactive questions

Look at the graph below and determine whether the function's rate of change is constant or not:

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FAQ

Everything you need to know about this question

How do I know which axis represents what?

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The x-axis (horizontal) shows time in minutes, and the y-axis (vertical) shows the amount of water. Always check the axis labels to be sure!

What if the point isn't exactly on a grid line?

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Look for the closest grid line or estimate between two values. In this graph, at 14 minutes the line hits exactly at the 160 mark on the y-axis.

Why does the graph have different slopes in different sections?

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Different slopes show different rates of water flow. Steeper sections mean water is being added faster, while horizontal sections mean no water is being added.

Do I need to calculate anything or just read the graph?

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For this problem, you just need to read the graph! Find 14 on the time axis, go straight up to the curve, then read across to the water amount axis.

What does the point C₁ represent on the graph?

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Point C₁ shows the starting point - at time 0 minutes, there are 0 units of water in the container. It's the beginning of our function.

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