Populations are often described by their doubling times. The doubling time is the amount of time it takes a population to double. We can calculate the doubling time of an increasing exponential model by examining its graph carefully. Since students seem to enjoy themodel for population growth on Gilligan’s Island, I like to use it to illustrate doubling in an exponential function. Continue reading “Doubling Time on Gilligan's Island”
Author: Dr Dave
What Should Have Happened on Gilligan's Island?
Last week the students in my College Algebra started exponential functions. They got started on the basics of exponential graphs, when they are increasing and decreasing, and exponentials with a base e. With these basics completed, they are working on an Applications Quiz this week. To get them started on this material, I introduced an application based on Gilligan’s Island.
Continue reading “What Should Have Happened on Gilligan's Island?”
Real Points of Inflection
Real world examples help students to see where the mathematics we teach them can be used. Let’s look at a real world example of a point of inflection.
From 2006 through 2011, Verizon Wireless has grown steadily. The table below illustrates the growth in revenue as well as connections (phone numbers).
Introducing Piecewise Functions
After weeks of linear functions, quadratic functions, and matrices, I needed an introductory example for piecewise functions. Examples like this catch student’s attention and get them thinking about how math might be used in real life. I used the example below in class and in the form you see below for my online classes.
How many of you have a car? How many of you have car insurance? In most of my classes, almost every student has a car and insurance. Yet many people are completely unfamiliar with how their insurance works and what they pay annually for that insurance.
For most people, the most important part of their insurance is the premium they pay every six months. A typical premium is $600 every 6 months. This premium may vary depending on the deductible amount. The deductible is the amount you must for a claim before the insurance company pays the rest of the claim. A higher deductible typically means a lower premium. Comparatively speaking, a lower deductible means a higher premium.
What Type of Technology to Require?
At my college, we have required students to have a graphing calculator for all classes at the Beginning Algebra level and above. Some of you might argue that this is overkill or that we should not be using any technology, but I am assuming that there must be some type of technology in the students hands. I teach College Algebra, Finite Math, and Business Calculus. Most of my students will not be moving on to a STEM major…so what technology is appropriate?