In 1965 Gordon Moore, computer scientist and Intel co-founder, predicted that computer processor speeds would double every two years. Twelve years later the first modern video game console, the Atari 2600, was released.

In this lesson, students write an exponential function based on the Atari 2600 and Moore's Law, and research other consoles to determine whether they've followed Moore's Law.

Students will

Apply an exponential growth model, stated verbally, to various inputs

Generalize with an exponential function to model processor speed for a given year

Research actual processor speeds, and compare them to the model's prediction

Calculate the annual growth rate of the model (given biannual growth rate)

Use technology to model the actual processor speeds with an exponential function

Interpret the components of the regression function in this context, and compare them to the model

Before you begin

Students should be familiar with the meaning of and notation for exponents, square roots, percent growth and the basics of exponential functions of the general form y = ab^{x}. Students will need to enter data in calculator lists and perform an exponential regression, so if they're inexperienced with this process, you will need time to demonstrate.

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Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF)

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Building Functions (BF), Interpreting Functions (IF)

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Topic:
Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI), Similarity, Right Triangles, and Trigonometry (SRT)

How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.

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Building Functions (BF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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Topic:
Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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Topic:
Building Functions (BF), Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE)

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Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF)

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Topic:
Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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Topic:
Building Functions (BF), Interpreting Functions (IF)

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Topic:
Interpreting Categorical and Quantitative Data (ID)

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Topic:
Building Functions (BF), Functions (F), Interpreting Functions (IF)

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Topic:
Interpreting Categorical and Quantitative Data (ID)

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Topic:
Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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Topic:
Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Reasoning with Equations and Inequalities (REI)

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Building Functions (BF), Interpreting Functions (IF), Using Probability to Make Decisions (MD)

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Topic:
Creating Equations (CED), Building Functions (BF), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

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Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

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Topic:
Building Functions (BF), Interpreting Functions (IF)

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Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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Linear, Quadratic, and Exponential Models (LE), Reasoning with Equations and Inequalities (REI)

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Topic:
Interpreting Categorical and Quantitative Data (ID)

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Topic:
Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)