As stated above, students should already be familiar with exponential functions prior to this lesson. Using the TI-83 graphing calculator to explore exponential functions would provide students with a basis of representing functions symbolically and graphically. The TI-83 has a split screen option that shows the graph of the function along with the table of values for the function. Hence, students get an opportunity to see how the table of values corresponds to the graph. One could also use the TI-83 to illustrate the concept of asymptotes.
Students can trace along the exponential graph by using the trace command to show an asymptote.
The table of values would show the y-coordinates getting smaller and smaller without reaching zero. Knowing the characterisitcs of exponential graphs will lead to interesting discussions about the limitations of mathematical modeling in the lesson that follows. Through this investigation, we will see how many atoms remain after a given number of half-lives during the radioactive decay of an isotope. Coins are a good representation of an atom since the atom either survives during the half-life or it decays. Divide the students into pairs and give each pair a shoebox along with 100 coins.