Temperature Function Analysis: Graphing Hot Water Cooling Over Time

Exponential Decay with Temperature Applications

Choose the graph that best describes the following:

Temperature of boiling water (Y) left to cool at room temperature as a function of time (X).

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Step-by-step written solution

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1

Understand the problem

Choose the graph that best describes the following:

Temperature of boiling water (Y) left to cool at room temperature as a function of time (X).

2

Step-by-step solution

The temperature of boiling water is roughly 100 degrees Celsius.

Room temperature is about 25 degrees.

Therefore, in the correct graph we will see a downward trend which will end above the X-axis (since the room is not frozen, the temperature will not reach 0).

The graph that describes this is graph C.

3

Final Answer

TimeTemperature'000

Key Points to Remember

Essential concepts to master this topic
  • Physical Rule: Hot objects cool rapidly at first, then slowly approach room temperature
  • Graph Shape: Exponential decay curve starts high at 100°C, curves down to 25°C
  • Check: Curve should never go below room temperature (stays above x-axis) ✓

Common Mistakes

Avoid these frequent errors
  • Choosing linear decrease instead of exponential decay
    Don't assume temperature drops at a constant rate = straight line graph! Real cooling follows Newton's Law - fast initial cooling that gradually slows down. Always choose the curved graph that shows rapid initial decrease then levels off at room temperature.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

Why doesn't the temperature drop in a straight line?

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Temperature difference drives cooling rate! When water is very hot (100°C vs 25°C room), it cools quickly. As it gets closer to room temperature, the difference gets smaller, so cooling slows down.

Will the water ever reach exactly room temperature?

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Theoretically, it approaches room temperature but never quite reaches it. However, for practical purposes, it gets very close to 25°C after enough time passes.

Why can't the graph go below the x-axis?

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The x-axis represents 0°C (freezing point). Since we're at room temperature (about 25°C), the water will never get colder than the surrounding air. The graph should level off above the x-axis.

How do I know which curve is steepest at the start?

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Look for the curve that drops most rapidly right after time = 0. Boiling water (100°C) has the biggest temperature difference from room temperature, so initial cooling should be very steep.

What if the room was colder, like 0°C?

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Then the curve would approach the x-axis (0°C) instead of staying well above it. The final temperature always matches the surrounding environment temperature.

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