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- Exponential Functions (20:00) This program compares quakes of various magnitudes that occurred in Sichuan Province to explain the difference between linear and exponential functions. The difference between magnitude and intensity, and their relation to each other, is also covered.
- Factoring (04:12) Substitution does not always work; if you can't substitute right away, try simplifying the function by factoring. Factoring is described and demonstrated.
- Inequalities (22:26) Venice has been prone to flooding for hundreds of years, but with the city sinking and sea levels worldwide rising, the situation in the 21st century is becoming dire. This program uses the design for a moveable floodgate, to be activated automatically when waters reach a critical level, to illustrate mathematical inequalities. Inequalities are also demonstrated by calculating the mpg of a hybrid and a gas-engine vehicle, factoring in both city and highway driving, to determine which is really more fuel efficient.
- Linear Functions (19:12) How much oil might Americans use in the near future? This program demonstrates data sets and linear functions by graphing current oil consumption and then using the data to predict future demand. Providing an overview of the slope formula, the slope-intercept form of a linear function, linear regression, and linear graphs, the video also explains linear functions in the context of cyclists pedaling up and down the hills of Tuscany. In addition, a linear model for heart rate during aerobics is used to generate an exercise data chart.
- Quadratic Functions (25:02) Quarterbacks have an intuitive grasp of quadratic functions—the path of a tossed football is a parabola, which is the graph of a quadratic function. In this program quadratic functions are used to model the arc of footballs and fireworks as they fall, and to determine how fast a car was moving at the time of an accident. In addition, a quadratic model for growth data charts a child’s change in height from birth to toddler. The roots of quadratic functions, quadratic regression, and solving quadratic equations are all covered.
- Systems of Equations (22:58) When Amazon.com began business in 1995 its expenses far outran its sales—the company wasn’t in the black until 2003. In this program, systems of equations are explained using Amazon’s rise to profitability, encryption, and ballistic missiles. In the first segment, a business’s break-even point is calculated, and in the next segment a substitution code, encrypted using linear equations, is deciphered. Last, a defense system proposed by Ronald Reagan to stop ICBMs in mid-air is shown to be based on quadratic equations.
- Variables and Equations (20:00) A decline in the population of honeybees, possibly due to colony collapse disorder, impacted the multimillion-dollar honey industry in 2006. This program investigates the bees’ changing population as part of an exploration of variables, expressions, and equations. Then, expressions are used to analyze a river’s meander ratio, or the ratio of its sinuous length to its straight-line length. The video includes a thorough explanation of the concept of equations, and how to solve for “x” in an algebraic expression.

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- Last Updated: Jan 4, 2023 9:13 AM
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