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Grade 12 Math Starter Lesson: Complex Function Models

By Newsela Staff
Last updated 2 months 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?

2.
What are the maximum and minimum temperatures throughout the day?

minimum: _______ºC
maximum: _______ºC
3.
As the temperature at the beach oscillates, the period of the function, or time it takes to return to the same temperature, is __________.
4.

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.


5.

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

Required
6.

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

7.

Order the temperatures at each time from lowest to highest.

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

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