The image you uploaded shows three tasks involving temperature measurements and financial analysis. Here’s a breakdown of each task based on the image:

Task 1:

• Data Given:

  • Time (minutes): 0, 2, 4, 6, 8, 10
  • Temperature (°C): 26, 35, 44, 53, 62, 71

• Questions:

  1. Write down the function rule that can be used to calculate the temperature using the given data points.
  2. Construct a suitable scale and graph the data as a function of time, plotting the temperature against time.
  3. From your graph, determine the temperature at 7 minutes and 15 seconds (7.25 minutes) and at 5.5 minutes.
  4. State the domain and range of the function.
  5. Explain whether the relationship between time and temperature is linear or non-linear. Justify your answer using your graph or the generated function rule.

Task 2:

• Scenario: A mortgage broker services a loan at a 5% rate for the first three hours and 1.5% per hour for every hour thereafter.

• Questions:

  1. Write down a function for the amount of interest as a function of the hours spent in servicing the loan.
  2. Plot the function on a graph and use it to determine how much interest is charged for servicing the loan for 5 hours.

Task 3:

• Scenario: The same service charge from Task 2 is now described differently, with a flat rate of 3% for the entire duration.

• Questions:

  1. Compare the total interest from Task 2 with the flat rate for a service time of 5 hours.
  2. Discuss which option would be better for the client based on the given service times and interest rates.

Next Steps

Would you like to focus on solving a specific task, or do you want an explanation of all the tasks?

Here are five relative questions that might deepen your understanding:

1. How do you determine whether a function is linear or non-linear just by looking at the data points?
2. What method can you use to derive the function rule from the temperature data?
3. How do you interpret the slope of the graph in the context of the temperature-time relationship?
4. What are the implications of the different interest rates over time in Task 2 versus Task 3?