Search the web for data sets that might be represented by each of the following families of functions: linear, quadratic, exponential, logarithmic. Create a web page where you briefly discuss and provide links to each of these sources. Then choose one of the data sources to explore further. Create (and provide a link to) an excel worksheet in which you show and discuss the data in at least three different forms (numeric, algebraic, and graphic). Explore and discuss ways that you could use this data with your students. Quadratic: A good example of data that fits a quadratic function is weather. Many travel sites have this data for different part of the world. The site I choose to explore pertains to the average temperatures in the Atlanta area. To view this data, click here.
Since temperatures usually increase throughout the spring and reach a maximum in the summer, only to decline again in the fall, this data fits a negative quadratic function. Below is the graph for the temperature in Atlanta, The smooth line is a representation of a quadratic curve and the plotted line is the actual data points.
As we can see by the above graph, although the data does not fit the quadratic curve perfectly, it is still a good representation of a quadratic function.
Exponential: Another form of data that can be found on the internet when discussing functions is exponential. Although there is not one definite type of data that fits this function all the time, as there is with quadratic, one example is the number of internet domains since 1998. You can view this data by clicking here.
Below is the graph reflecting the internet domains. As most would expect, information dealing with the internet is exponential. Notice from the graph that the curve starts close to the x axis and then increases dramatically.
Logarithmic: A third function that can be explored using data sets is logarithmic. Like the exponential function, logarithmic functions are not prevelent in any one type of data set. However, one example is the number of injuries in the workplace. You can view this data at the Center for Disease Control by clicking here.
The graph below shows the model for the logarithmic curve along with the actual data regarding injuries in the agricultural occupation. This data is per 100 full time employees. Notice that the blue curve is the actual data and the red curve is the model. As a typical logarithmic curve, this data increases, rapidly at first, and then slows its increase.
Linear: The final type of funtion that I found from the internet is linear data. It is interesting to note that the linear data found pertains to the growth of the United States population. To view this data, click here.
We will now discuss the different ways to use this data set, and how to incorporate this use in the classroom. This discussion is in the form of an excel worksheet.
Many different types of data can be found on the internet to use as teaching aids. This data can be used when teaching functions in addition to teaching statistics. Typically, when teachers think of obtaining and graphing data points, it is thought to be relevent to statistics only. Yet, once the data sets are explored further, one can realize the crossover to other topics in mathematics.