XBOX Xponential - UPDATED!
How have video game console speeds changed?
In this lesson, students write exponential functions to model Moore's prediction and the observed growth rate, and they discuss potential consequences should video games eventually become indistinguishable from reality.
Students will
- Write an exponential function to a model a verbal prediction for the growth of processor speeds.
- Describe how processor speeds have actually changed using an exponential model.
- Discuss the implications should video games become indistinguishable from reality.
Before you begin
Students need to be familiar with exponents. It's helpful if they know how to construct a basic exponential function, but they do not have to have this skill prior to the lesson.Common Core Standards
Content Standards
Mathematical Practices
Downloads
Related Lessons
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 - Legacy Version
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 - Legacy Version
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.
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.
Romeo & Juliet
How does two people's love for one another change over time? Students investigate the effect of coefficients on recursive functions, and explore whether or not romance can be modeled with mathematics.
Sharper Image
Should you buy a camera lens with vibration reduction? Students interpret graphs and use right triangle trigonometry to explore the relationship between focal length, viewing angle, and blurriness.
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.
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.
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.
House of Pain
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.
Pandemic - Updated!
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.
