Linear Functions
In this episode of Algebra Applications, three real-world explorations of linear functions are developed:

Sports
The relationship between slope and grade in cycling. Go on a tour of Italy through the mountains of Tuscany and apply students' understanding of slope.

Oil Exploration
The potential for oil exploration in the controversial Alaska National Wildlife Refuge (ANWR). A linear regression of oil consumption data over the past 25 years reveals an interesting pattern. How could new oil fields like ANWR help in breaking our dependence on foreign oil?

Medicine
Exercise needs to become a consistent part of everyone's lifestyle. In particular, aerobic exercises, which vigorously exerts the heart, is an important form of exercise. The maximum heart rate from aerobic exercise is a linear function dependent on age. Students are asked to develop a data table based on the function.

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Quadratic Functions
In this episode of Algebra Applications, three real-world explorations of linear functions are developed:

Pyrotechnics
Fireworks displays are elegant examples of quadratic function. In this segment the basics of quadratic functions in standard form are developed visually and students are guided through the planning of a fireworks display.

Forensics
The distance a car travels even after the brakes are applied can be described through a quadratic function. But there is also the reaction time, the split second before the brakes are applied. The total distance is known as the stopping distance and this segment analyzes the quadratic function. This is an equation that can be used by accident investigators.

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Variables and Equations
In this episode of Algebra Applications, two real-world explorations are developed:

Biology
Honey bees not only produce a tasty treat, they also help pollinate flowering plants that provide much of the food throughout the world. So, when in 2006 bee colonies started dying out, scientists recognized a serious problem. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder. Key math concepts covered include variables, equations, formulas, ratios and proportions, and box and whisker plots. Students use the Lists and Spreadsheets, Calculator, and Statistics features of the TI-Nspire.

Geology
Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river’s length to its straight-line distance tell us? In this segment the geological forces that account for a river’s motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to p. Key math concepts covered include variables, equations, ratios, geometry and measurement, statistical mean, and data analysis. Students use the Geometry, Lists and Spreadsheets, and Calculator features of the TI-Nspire.

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Functions and Relations
In this episode of Algebra Applications a simulated future journey to Mars offers a way of exploring conic sections, and their underlying functions. Students use the Graphs and Geometry features of the TI-Nspire.

Parabolic paths
The liftoff and pre-orbital path of the rock is described by a parabola. Students explore the properties of parabolas from the standpoint of the parametric equations that describe the horizontal and vertical directions of motion for the rocket.

Circular paths
The path of a rocket orbiting the Earth can be modeled with the equation of a circle. Students explore the quadratic relation and the parametric equations that can be used to model the path of a spacecraft orbiting Earth.

Elliptical paths
The planets orbiting the sun follow elliptical paths. In fact, the trajectory of a spacecraft traveling to Mars would also be elliptical. Students explore these various ellipses.

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Inequalities
In this episode of Algebra Applications, two real-world explorations of inequalities are developed:

Hybrid Cars
With the increasing demand worldwide for cars, the cost of gasoline continues to rise. The need for fuel-efficient cars makes hybrids a current favorite. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Students use the Graphs and Geometry features of the TI-Nspire.

Floods in Venice
The city of Venice is slowly sinking into the Adriatic Sea. So what does a city whose streets are full of water do about flooding? Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding, rising sea levels, and sinking have on this grand, ancient city. Students use the Lists and Spreadsheets and the Program Editor features of the TI-Nspire.

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Exponential Functions
In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis.

What is an earthquake?
The basic definition of an exponential function is shown in the intensity function for an earthquake. Students analyze data and perform an exponential regression based on data from the Sichuan earthquake.

What is the difference between earthquake intensity and magnitude?
An exponential model describes the intensity of an earthquake, while a logarithmic model describes the magnitude of an earthquake. In the process students learn about the inverse of an exponential function.

How is earthquake magnitude measured?
An earthquake is an example of a seismic wave. A wave can be modeled with a trigonometric function. Using the TI-Nspire, students link the amplitude to an exponential function to analyze the dramatic increase in intensity resulting from minor changes to magnitude.

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Data Analysis and Probability
In this episode of Algebra Applications, students explore the dramatic events of 2008 related to the mortgage crisis. Brought about principally through mortgage defaults, the effect on the overall economy was severe. Yet, this situation offers an ideal case study for the exploration of key concepts in data analysis and probability. By exploring these questions students get a front row seat to the historical events of the world’s largest economy.

What is a mortgage?
The time value of money is at the basis of all loans. Students learn about the key factors that determine monthly mortgage payments and use the TI-Nspire to create an amortization table. This table is used throughout the rest of the program to explore different scenarios.

What is a subprime mortgage?
Having learned the general features of a mortgage, students learn the specifics of a subprime mortgage. With this comes the notion of a credit score, and with credit scores come the probabilities for a loan default. Students use the amortization table to run probability simulations to determine possible loan defaults on subprime mortgages.

What is an adjustable rate mortgage?
Another factor in the mortgage crisis was the use of adjustable rate mortgages Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis.

Systems of Equations
In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of systems of equations. Such disparate phenomena as profit and loss, secret codes, and ballistic missile shields can be explored through systems of equations.

Business
. Profit and loss are the key measures in a business. A system of equations that includes an equation for income and one for expenses can be used to determine profit and loss. Students solve a system graphically.

Forensics
Secret codes and encryption are ideal examples of a system of equations. In this activity, students encrypt and decrypt a message.

Ballistics
A ballistic missile shield allows you to shoot incoming missiles out of the sky. Mathematically, this is an example of a linear-quadratic system. Students graph such a system and find the points of intersection between a line and a parabola.

Rational Functions
In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of rational functions. Such disparate phenomena as submarines, photography, and the appearance of certain organisms can be explained through rational function models.

Engineering
In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine.

Biology
All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms.

Photography
Even though digital cameras make traditional cameras obsolete, some of the lessons from film cameras are useful for digital photography. In particular, the inverse square law, which is a rational function, can help explain lighting, lenses, and distance between camera and subject.

Logarithmic Functions
In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of logarithmic functions. Such disparate phenomena as hearing loss and tsunamis can be explained through logarithmic models.

What are logarithms?
The mathematical definition of a logarithm is the inverse of an exponential function, but why do we need to use logarithms? This segment explains the nature of some data sets, where incremental changes in the domain result in explosive changes in the range. As a result, logarithms allow for the a way to present and analyze what would otherwise be unwieldy data.

Hearing loss
We live in a noisy world. In fact, prolonged exposure to noise can cause hearing loss. Students analyze the noise level at a rock concert and determine the ideal distance where the noise level is out of the harmful range. Using the TI-Nspire’s Geometry tools, student create a mathematical simulation of the decibel level as a function of distance.

The New Guinea tsunami
In 1998 a devastating tsunami was triggered by a 7.0 magnitude earthquake off the coast of New Guinea. The amount of energy from this earthquake was equivalent to a thermonuclear explosion. Students analyze the energy outputs for different magnitude earthquakes. Using the Graphing tools, students explore the use of a logarithmic scale to better analyze exponential data.