Grade 12 Math Starter Lesson: Complex Function Models
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Last updated over 1 year ago
8 questions
Note from the author:
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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.
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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.
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Required
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Question 8
8.
Answer the Essential Question: How can function models help us make predictions?
Question 1
1.
Question 2
2.
What are the maximum and minimum temperatures throughout the day?
minimum: _______ºC
maximum: _______ºC
Question 3
3.
As the temperature at the beach oscillates, the period of the function, or time it takes to return to the same temperature, is __________.
Question 4
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.
Question 5
5.
What is the maximum temperature in a single 24 hour day in \degree C? Round to the nearest tenth of a degree.
Question 6
6.
Question 7
7.
What is the temperature as people arrive at the beach at 10 A.M. in \degree C?
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At noon, it is hotter in the desert than at the beach.
True
False
Order the temperatures at each time from lowest to highest.
