Grade 12 Math Starter Lesson: Complex Function Models

Last updated almost 2 years ago

8 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

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?

Akwankyerɛ

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?

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

Grade 12 Math Starter Lesson: Complex Function Models

Last updated almost 2 years ago

8 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

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?

Akwankyerɛ

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

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

Ɛhia

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

Nokorɛ

Ɛnyɛ ampa

Order the temperatures at each time from lowest to highest.

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

Grade 12 Math Starter Lesson: Complex Function Models

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

Grade 12 Math Starter Lesson: Complex Function Models

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

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.

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.

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.