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?

Instructions

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?

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?

Instructions

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.

What are the maximum and minimum temperatures throughout the day?

minimum: _______ºC 
maximum: _______ºC 

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

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.

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

Required

Grade 12 Math Starter Lesson: Complex Function Models

Grade 12 Math Starter Lesson: Complex Function Models

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

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

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

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.

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

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

Order the temperatures at each time from lowest to highest.

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

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

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.

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

Order the temperatures at each time from lowest to highest.