Content Showcase: Video Library

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.

The mathematical definition of a logarithm is the inverse of an exponential function, but why do we need to use logarithms?

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.

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.

In this episode of Algebra Applications, three real-world explorations of quadratic functions are developed: Pyrotechnics. Fireworks displays are elegant examples of quadratic functions. Forensics.

An overview of the key topics to be covered in the video.

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.

From the time a baby is born to the time it reaches 36 months of age, there is dramatic growth in height and weight. An analysis of CDC data reveals a number of quadratic models that doctors can use to monitor the growth and development of children.

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.

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.

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.

The Hubble Telescope has transformed how we view the universe. We learn about the lens formula and how it is used in the construction of telescopes.

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.

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.

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

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.

In this episode of Algebra Applications, two real-world explorations are developed: Biology. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder. Geology.