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Grade 12 Math Starter Lesson: Complex Function Models

Last updated over 1 year ago
8 questions
Note from the author:
In this lesson, you will compare the temperature at two different locations using complex functions to model temperature over time.

Essential Question: How can function models help us make predictions?
In this lesson, you will compare the temperature at two different locations using complex functions to model temperature over time.

Essential Question: How can function models help us make predictions?
The temperature at the beach varies throughout the day. The temperatures vary according to the sinusoidal function:
A(t)= 19+6sin (\pi (t - \dfrac{1}{2}))
where t is the temperature (ºC) and A(t) is the time in hours past midnight.

1

What is the temperature as people arrive at the beach at 10 A.M. in \degree C?

1
What are the maximum and minimum temperatures throughout the day?

minimum: _______ºC
maximum: _______ºC
1
As the temperature at the beach oscillates, the period of the function, or time it takes to return to the same temperature, is __________.
1

Sketch a graph of the temperature at the beach throughout the day. Let the y-axis represent \degree C and the x-axis be time since midnight.

The temperature in the desert is modeled by the function B(t)=\dfrac{35t(t-5)}{t^2+8t+16} + 17, where t is the temperature (°𝐶) and A(t) is the time in hours past midnight.


1

What is the maximum temperature in a single 24 hour day in \degree C? Round to the nearest tenth of a degree.

Required
1

At noon, it is hotter in the desert than at the beach.

1

Order the temperatures at each time from lowest to highest.

  1. Temperature in the desert at 5 P.M.
  2. Temperature at the beach at 4:30 P.M.
  3. Temperature in the desert at 8 A.M.
  4. Temperature in the desert at 11 A.M.
  5. Temperature at the beach at 9 A.M.
  6. Temperature at the beach at noon
1

Answer the Essential Question: How can function models help us make predictions?