XBOX Xponential
How have video game console speeds changed over time?
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 = abx. 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.Common Core Standards
Content Standards
Mathematical Practices
Downloads
Additional Materials
- Graphing calculators
- Computers with Internet access
Related Lessons
Connected
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.
Carpe Donut
How much should people pay for donuts? Students use linear, rational, and piecewise functions to describe the total and average costs of an order at Carpe Donut.
Sofa Away From Me
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.
Pyramid of Sleaza
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.
Pandemic
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.
Loan Ranger
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.
Fall of Javert
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.
I Remember
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.
Going Once, Going Twice
How much should you bid in an auction? Students use probability, expected value, and polynomial functions to develop a profit-maximizing bidding strategy.
iPod dPreciation
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.
Hitting the Slopes
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.
It's a Date
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.
Win At Any Cost?
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.
Pounding Headache
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.
Green Acres
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.
Driving Question
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.
Wiibates
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.
Pizza Pi (HS)
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.
Financial Aid
How much more do graduates earn, and is college worth the cost? Students use systems of linear equations to compare different educational options.
The Sound of Silence
How do noise-canceling headphones work? In this lesson, students use transformations of trigonometric functions to explore how sound waves can interfere with one another, and how noise-canceling headphones use incoming sounds to figure out how to produce that sweet, sweet silence.
Prescripted
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.
Wage War
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.
Pic Me
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.
Billions and Billions
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.