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

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.

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

Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population. They'll also informally prove that vampires can't be real.

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

How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.

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

Could Inspector Javert have survived the fall? Students use quadratic models to determine how high the bridge was in Les Misérables, and explore the maximum height from which someone can safely jump.

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

How much can you trust your memory? Students construct and compare linear and exponential models to explore how much a memory degrades each time it's remembered.

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

How much should you bid in an auction? Students use probability, expected value, and polynomial functions to develop a profit-maximizing bidding strategy.

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

How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.

Can you predict a country's Winter Olympic performance? Students analyze scatterplots and correlation coefficients to pick out the best predictive model for Olympic success.

Topic:
Interpreting Categorical and Quantitative Data (ID)

How can we improve our calendar? Students examine some other ways to keep track of dates, and use number sense and function concepts to convert between different calendars.

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

How should sports teams spend their money to win more games? Students look at data for four major pro sports leagues to find out whether it's possible to buy wins.

Topic:
Interpreting Categorical and Quantitative Data (ID)

How much Tylenol can you safely take? Students use exponential functions and logarithms to explore the risks of acetaminophen toxicity, and discuss what they think drug manufacturers should do to make sure people use their products safely.

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

How has the urban population changed over time, and will we all eventually live in cities? Students use recursive rules along with linear and exponential models to explore how America's urban areas have been growing over the last 200 years.

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

When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.

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

How much should Nintendo charge for the Wii U? Students use linear functions to explore demand for the Wii U console and Nintendo's per-unit profit from each sale. They use those functions to create a quadratic model for Nintendo's total profit and determine the profit-maximizing price for the console.

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

Which size pizza should you order? Students apply the area of a circle formula to write linear and quadratic formulas that measure how much of a pizza is actually pizza, and how much is crust.

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)

How should pharmaceutical companies decide what to develop? In this lesson, students use linear and quadratic functions to explore how much pharmaceutical companies expect to make from different drugs, and discuss ways to incentivize companies to develop medications that are more valuable to society.

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

How much should companies pay their employees? Students graph and solve systems of linear equations in order to examine the effects of wage levels on labor and consumer markets, and they discuss the possible pros and cons of increasing the minimum wage.

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

How can you become popular on Instagram? Students use linear regression models and correlation coefficients to evaluate whether having more followers, posts, and hashtags actually make pictures more popular on Instagram.

Topic:
Interpreting Categorical and Quantitative Data (ID)

How has the human population changed over time? Students build an exponential model for population growth and use it to make predictions about the future of our planet.

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

Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.

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

Why are so many Americans dying from opiate overdoses? Students use exponential decay and rational functions to understand why addicted patients seek more and stronger opioids to alleviate their pain.

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