Graph labels and scales | Modeling | Algebra II | Khan Academy | Summary and Q&A

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June 30, 2020
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Graph labels and scales | Modeling | Algebra II | Khan Academy

TL;DR

Chloe models the relationship between the temperature of a pizza and the time it takes to defrost it.

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Key Insights

  • πŸ˜’ Chloe uses an equation to model the temperature of a defrosting pizza as a function of time.
  • πŸ›€ The graph shows that the temperature of the pizza starts at a negative value and gradually increases over time.
  • ❣️ The x-axis represents time in minutes, while the y-axis represents temperature in degrees Celsius.
  • ☺️ The domain of the graph is restricted to x β‰₯ 0 and x < 25, focusing on the first 25 minutes of defrosting.

Transcript

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Questions & Answers

Q: How does Chloe model the relationship between the temperature of the pizza and the time it takes to defrost it?

Chloe uses the equation P = 20 - 25 * (0.8^T) to model the temperature of the pizza as a function of time. This equation takes into account the starting temperature (20 degrees Celsius) and the rate at which the pizza warms up (-25 * 0.8^T).

Q: What are the labels for the axes in Chloe's graph?

The x-axis is labeled as T, representing time in minutes. The y-axis is labeled as P, representing temperature in degrees Celsius.

Q: What does the negative temperature on the graph represent?

The negative temperature on the graph represents the initial temperature of the pizza when it is taken out of the freezer. Since the pizza is below freezing when it is first defrosted, the temperature is negative.

Q: Why is it important to restrict the domain of the graph to x β‰₯ 0 and x < 25?

Restricting the domain to x β‰₯ 0 and x < 25 ensures that we are only considering the first 25 minutes of defrosting. Since we are modeling the temperature as a function of time, negative time values are not meaningful in this context, and we only want to focus on the initial defrosting period.

Summary & Key Takeaways

  • Chloe models the relationship between the temperature of a pizza and the time it takes to defrost it.

  • She uses the equation P = 20 - 25 * (0.8^T) to represent the temperature of the pizza as a function of time.

  • Chloe graphs the relationship using a graphing calculator and discusses the labels for the axes and the range and domain of the graph.

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