Exponential Functions on the Web
The below were collected for a presentation by Esther Billings and John Golden at
Grand Valley State's Science and Math Update Seminar.
The presentation was on a penny toss for modeling exponential functions, and various
pedagogical issues concerning the teaching of exponential functions. If you prefer to click
rather than type,
these links are available on the web at http://www2.gvsu.edu/~goldenj/exponential.html
Wind Chill: A teacher developed lesson based on modeling wind chill temperature vs. wind speed as an exponential function. Their examples are given using the Casio CFX-9800G graphing calculator,
but are easily adapted to TI models. Note that windchill is actually a linear + a root function of
windspeed, given by: WC = 91.4 - (0.474677 - 0.020425 * V + 0.303107 * SQRT(V)) * (91.4 - T)
WC = wind chill index,
V = wind speed (mph), and
T = temperature (° F). So there are some issues with the regression.
Exponential Explorations: A California middle school teacher developed group of lessons exploring exponential growth as compared to linear growth. She has four activities based on websites on the following
1.Invasive Weeds: A Growing Pain,
2.Monthly Payments on a $100,000 Mortgage,
3.World Population Study, and
4.Average Height of Children.
Each is accompanied by a student worksheet.
Mile Run Record: an extensive online lesson utilizing the web and Excel worksheets. Using the motivating problem of predicting the record times for running the mile, it guides students through exponential curve fitting on various data sets before applying the techniques to the mile. There is also a variation on the penny toss using M&M's or skittles. Sounds sweet.
Million $ Mission: a variation on the classic problem of rice on a chessboard (One grain on the first square, two on the next, four
on the third,...) by a math teacher now working in outreach for Rice University. (Coincidence?)
Hired for a 30 day job a student has the choice of: 1.One cent on the first day, two cents on the second day, and double your salary every day thereafter for the thirty days; or
2.Exactly $1,000,000. (That's one million dollars!)
Towers of Hanoi: a rather boring
description of a nice problem: finding a pattern to the minimum number of moves to solve the Towers of Hanoi puzzle vs. the number of disks. There's a legend that somewhere (in Hanoi, presumably) there is a Buddhist monk working on a 64 disk tower problem. When he is done,
the world ends. How long will it take? Does he have modern computational methods?
a nice activity requiring access to the web or a Blue Book and a used car circular. Students
use exponential regression to determine fair used car prices. Very innovative. Better for a
large scale project than an in class lesson.
Space Exponentials: Actual exponential and logarithmic problems that have come up in NASA. Some are, expectedly, quite complicated. There is quite a bit of real life application for other
function types also, at NASA SPACE MATHEMATICS page.